# Category: Estimation theory

Shrinkage (statistics)
In statistics, shrinkage is the reduction in the effects of sampling variation. In regression analysis, a fitted relationship appears to perform less well on a new data set than on the data set used f
Kullback's inequality
In information theory and statistics, Kullback's inequality is a lower bound on the Kullback–Leibler divergence expressed in terms of the large deviations rate function. If P and Q are probability dis
97.5th percentile point
In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96, mea
Proof of Stein's example
Stein's example is an important result in decision theory which can be stated as The ordinary decision rule for estimating the mean of a multivariate Gaussian distribution is inadmissible under mean s
Likelihood principle
In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelih
Average treatment effect
The average treatment effect (ATE) is a measure used to compare treatments (or interventions) in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the di
Regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'l
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 Tibshir
Nuisance parameter
In statistics, a nuisance parameter is any parameter which is unspecified but which must be accounted for in the hypothesis testing of the parameters which are of interest. The classic example of a nu
Endogeneity (econometrics)
In econometrics, endogeneity broadly refers to situations in which an explanatory variable is correlated with the error term. The distinction between endogenous and exogenous variables originated in s
Set identification
In statistics and econometrics, set identification (or partial identification) extends the concept of identifiability (or "point identification") in statistical models to situations where the distribu
Cramér–Rao bound
In estimation theory and statistics, the Cramér–Rao bound (CRB) expresses a lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter, the variance of any
Point estimation
In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best
Observed information
In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function
CDF-based nonparametric confidence interval
In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculat
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 p
Efficiency (statistics)
In statistics, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, needs fewer input data or o
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. The parameters describe an underlying phys
Location estimation in sensor networks
Location estimation in wireless sensor networks is the problem of estimating the location of an object from a set of noisy measurements. These measurements are acquired in a distributedmanner by a set
MINQUE
In statistics, the theory of minimum norm quadratic unbiased estimation (MINQUE) was developed by C. R. Rao. Its application was originally to the problem of heteroscedasticity and the estimation of v
Parameter space
The parameter space is the space of possible parameter values that define a particular mathematical model, often a subset of finite-dimensional Euclidean space. Often the parameters are inputs of a fu
Generalized pencil-of-function method
Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting information with complex exponentials. Being si
Stein's example
In decision theory and estimation theory, Stein's example (also known as Stein's phenomenon or Stein's paradox) is the observation that when three or more parameters are estimated simultaneously, ther
Parameter identification problem
In economics and econometrics, the parameter identification problem arises when the value of one or more parameters in an economic model cannot be determined from observable variables. It is closely r
Coverage probability
In statistics, the coverage probability is a technique for calculating a confidence interval which is the proportion of the time that the interval contains the true value of interest. For example, sup
U-statistic
In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise natura
Sheppard's correction
In statistics, Sheppard's corrections are approximate corrections to estimates of moments computed from binned data. The concept is named after William Fleetwood Sheppard. Let be the measured kth mome
Confidence and prediction bands
A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Similarly, a prediction band is used to represent t
Rao–Blackwell theorem
In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result which characterizes the transformation of an arbitrarily crude estimator into an es
Confidence region
In statistics, a confidence region is a multi-dimensional generalization of a confidence interval. It is a set of points in an n-dimensional space, often represented as an ellipsoid around a point whi
Relaxed intersection
The relaxed intersection of m sets corresponds to the classicalintersection between sets except that it is allowed to relax few sets in order to avoid an empty intersection.This notion can be used to
Confidence distribution
In statistical inference, the concept of a confidence distribution (CD) has often been loosely referred to as a distribution function on the parameter space that can represent confidence intervals of
Estimation
Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The va
Richardson–Lucy deconvolution
The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was
Statistical learning theory
Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem
Linear regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables)
Fisher consistency
In statistics, Fisher consistency, named after Ronald Fisher, is a desirable property of an estimator asserting that if the estimator were calculated using the entire population rather than a sample,
Set estimation
In statistics, a random vector x is classically represented by a probability density function. In a set-membership approach or set estimation, x is represented by a set X to which x is assumed to belo
Estimand
An estimand is a quantity that is to be estimated in a statistical analysis. The term is used to more clearly distinguish the target of inference from the method used to obtain an approximation of thi
Matrix regularization
In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to
Lehmann–Scheffé theorem
In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. The theorem states that any estima
Identifiability
In statistics, identifiability is a property which a model must satisfy for precise inference to be possible. A model is identifiable if it is theoretically possible to learn the true values of this m
V-statistic
V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. V-statistics are closely related to U-statistics (
Chapman–Robbins bound
In statistics, the Chapman–Robbins bound or Hammersley–Chapman–Robbins bound is a lower bound on the variance of estimators of a deterministic parameter. It is a generalization of the Cramér–Rao bound
Formation matrix
In statistics and information theory, the expected formation matrix of a likelihood function is the matrix inverse of the Fisher information matrix of , while the observed formation matrix of is the i
Data assimilation
Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – fo
Empirical probability
The empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a
Estimation statistics
Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, anal