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92 relations: Adrien-Marie Legendre, Age of Discovery, Alexander Aitken, Arithmetic mean, Astronomy, Bayesian statistics, Best linear unbiased prediction, Bias, Carl Friedrich Gauss, Central limit theorem, Ceres (dwarf planet), Closed-form expression, Compressed sensing, Confidence interval, Convex optimization, Correlation and dependence, Correlation does not imply causation, Covariance matrix, Curve fitting, Degrees of freedom (statistics), Dependent and independent variables, Elastic net regularization, Errors and residuals, Errors-in-variables models, Estimation theory, Expected value, Exponential family, Fisher information, Franz Xaver von Zach, Gauss' method, Gauss–Markov theorem, Gauss–Newton algorithm, Gauss–Seidel method, Generalized least squares, Generalized linear model, Geodesy, Giuseppe Piazzi, Gradient, Hadamard product (matrices), Heteroscedasticity, Hooke's law, Jacobian matrix and determinant, Journal of the Royal Statistical Society, Jupiter, Kepler's laws of planetary motion, Lagrange multiplier, Laplace distribution, Least absolute deviations, Least squares adjustment, Least-angle regression, ..., Libration, Linear combination, Linear least squares (mathematics), Linearity, Loss function, Maxima and minima, Maximum likelihood estimation, Measurement uncertainty, Method of moments (statistics), Minimum mean square error, Non-linear least squares, Norm (mathematics), Normal distribution, Ordinary least squares, Overdetermined system, Pierre-Simon Laplace, Polynomial least squares, Principal component analysis, Prior probability, Probability, Probability density function, Probability distribution, Projection (linear algebra), Proximal gradient methods for learning, Quadratic programming, Regression analysis, Regularization (mathematics), Robert Adrain, Roger Cotes, Roger Joseph Boscovich, Root mean square, Saturn, Squared deviations from the mean, Statistical hypothesis testing, Taxicab geometry, Taylor series, Tikhonov regularization, Tobias Mayer, Total least squares, Uncorrelated random variables, Variance, Whitening transformation. Expand index (42 more) »
Adrien-Marie Legendre
Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.
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Age of Discovery
The Age of Discovery, or the Age of Exploration (approximately from the beginning of the 15th century until the end of the 18th century) is an informal and loosely defined term for the period in European history in which extensive overseas exploration emerged as a powerful factor in European culture and was the beginning of globalization.
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Alexander Aitken
Alexander Craig "Alec" Aitken (1 April 1895 – 3 November 1967) was one of New Zealand's greatest mathematicians.
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Arithmetic mean
In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.
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Astronomy
Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.
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Bayesian statistics
Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief known as Bayesian probabilities.
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Best linear unbiased prediction
In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects.
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Bias
Bias is disproportionate weight in favour of or against one thing, person, or group compared with another, usually in a way considered to be unfair.
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
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Central limit theorem
In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.
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Ceres (dwarf planet)
Ceres (minor-planet designation: 1 Ceres) is the largest object in the asteroid belt that lies between the orbits of Mars and Jupiter, slightly closer to Mars' orbit.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Compressed sensing
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.
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Confidence interval
In statistics, a confidence interval (CI) is a type of interval estimate, computed from the statistics of the observed data, that might contain the true value of an unknown population parameter.
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Convex optimization
Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
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Correlation and dependence
In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.
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Correlation does not imply causation
In statistics, many statistical tests calculate correlations between variables and when two variables are found to be correlated, it is tempting to assume that this shows that one variable causes the other.
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Covariance matrix
In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.
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Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
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Degrees of freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Elastic net regularization
In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods.
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Errors and residuals
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value".
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Errors-in-variables models
In statistics, errors-in-variables models or measurement error models are regression models that account for measurement errors in the independent variables.
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Estimation theory
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component.
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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Exponential family
In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below.
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Fisher information
In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.
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Franz Xaver von Zach
Baron Franz Xaver von Zach (Franz Xaver Freiherr von Zach) (4 June 1754 – 2 September 1832) was a Hungarian astronomer born at Pest, Hungary (now Budapest in Hungary).
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Gauss' method
In orbital mechanics (subfield of celestial mechanics), Gauss's method is used for preliminary orbit determination from at least three observations (more observations increases the accuracy of the determined orbit) of the orbiting body of interest at three different times.
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Gauss–Markov theorem
In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator, provided it exists.
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Gauss–Newton algorithm
The Gauss–Newton algorithm is used to solve non-linear least squares problems.
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Gauss–Seidel method
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.
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Generalized least squares
In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model.
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Generalized linear model
In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution.
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Geodesy
Geodesy, also known as geodetics, is the earth science of accurately measuring and understanding three of Earth's fundamental properties: its geometric shape, orientation in space, and gravitational field.
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Giuseppe Piazzi
Giuseppe Piazzi (16 July 1746 – 22 July 1826) was an Italian Catholic priest of the Theatine order, mathematician, and astronomer.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Hadamard product (matrices)
In mathematics, the Hadamard product (also known as the Schur product or the entrywise product) is a binary operation that takes two matrices of the same dimensions, and produces another matrix where each element i,j is the product of elements i,j of the original two matrices.
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Heteroscedasticity
In statistics, a collection of random variables is heteroscedastic (or heteroskedastic; from Ancient Greek hetero “different” and skedasis “dispersion”) if there are sub-populations that have different variabilities from others.
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Hooke's law
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Journal of the Royal Statistical Society
The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.
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Jupiter
Jupiter is the fifth planet from the Sun and the largest in the Solar System.
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Kepler's laws of planetary motion
In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.
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Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).
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Laplace distribution
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.
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Least absolute deviations
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute value (LAV), least absolute residual (LAR), sum of absolute deviations, or the ''L''1 norm condition, is a statistical optimality criterion and the statistical optimization technique that relies on it.
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Least squares adjustment
Least squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals.
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Least-angle regression
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.
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Libration
In astronomy, libration is a perceived oscillating motion of orbiting bodies relative to each other, notably including the motion of the Moon relative to Earth, or of trojan asteroids relative to planets.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Linear least squares (mathematics)
In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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Loss function
In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.
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Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity.
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Method of moments (statistics)
In statistics, the method of moments is a method of estimation of population parameters.
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Minimum mean square error
In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable.
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Non-linear least squares
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n).
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Ordinary least squares
In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model.
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Overdetermined system
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.
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Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.
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Polynomial least squares
In mathematical statistics, polynomial least squares comprises a broad range of statistical methods for estimating an underlying polynomial that describes observations.
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Principal component analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.
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Prior probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.
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Probability
Probability is the measure of the likelihood that an event will occur.
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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
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Proximal gradient methods for learning
Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable.
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Quadratic programming
Quadratic programming (QP) is the process of solving a special type of mathematical optimization problem—specifically, a (linearly constrained) quadratic optimization problem, that is, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.
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Regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.
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Regularization (mathematics)
In mathematics, statistics, and computer science, particularly in the fields of machine learning and inverse problems, regularization is a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting.
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Robert Adrain
Robert Adrain (30 September 1775 – 10 August 1843) was an Irish mathematician, whose career was spent in the USA.
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Roger Cotes
Roger Cotes FRS (10 July 1682 – 5 June 1716) was an English mathematician, known for working closely with Isaac Newton by proofreading the second edition of his famous book, the Principia, before publication.
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Roger Joseph Boscovich
Roger Joseph Boscovich (Ruđer Josip Bošković,, Ruggiero Giuseppe Boscovich, Rodericus Iosephus Boscovicus; 18 May 1711 – 13 February 1787) was a Ragusan physicist, astronomer, mathematician, philosopher, diplomat, poet, theologian, Jesuit priest, and a polymath, Fairchild University website.
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Root mean square
In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).
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Saturn
Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter.
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Squared deviations from the mean
Squared deviations from the mean (SDM) are involved in various calculations.
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Statistical hypothesis testing
A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.
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Taxicab geometry
A taxicab geometry is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Tikhonov regularization
Tikhonov regularization, named for Andrey Tikhonov, is the most commonly used method of regularization of ill-posed problems.
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Tobias Mayer
Tobias Mayer (17 February 1723 – 20 February 1762) was a German astronomer famous for his studies of the Moon.
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Total least squares
In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account.
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Uncorrelated random variables
In probability theory and statistics, two real-valued random variables, X,Y, are said to be uncorrelated if their covariance, E(XY) − E(X)E(Y), is zero.
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Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
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Whitening transformation
A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1.
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References
[1] https://en.wikipedia.org/wiki/Least_squares
