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Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other quantiles) of the response variable.
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
Such an estimator is not necessarily an M-estimator of ρ-type, but if ρ has a continuous first derivative with respect to , then a necessary condition for an M-estimator of ψ-type to be an M-estimator of ρ-type is (,) = (,). The previous definitions can easily be extended to finite samples.
The Theil–Sen estimator is a simple robust estimation technique that chooses the slope of the fit line to be the median of the slopes of the lines through pairs of sample points. It has similar statistical efficiency properties to simple linear regression but is much less sensitive to outliers .
A Rao–Blackwell estimator δ 1 (X) of an unobservable quantity θ is the conditional expected value E(δ(X) | T(X)) of some estimator δ(X) given a sufficient statistic T(X). Call δ(X) the "original estimator" and δ 1 (X) the "improved estimator". It is important that the improved estimator be observable, i.e. that it does not depend on θ.
Thus, we postulate that the conditional expectation of given is a simple linear function of , {} = +, where the measurement is a random vector, is a matrix and is a vector. This can be seen as the first order Taylor approximation of E { x ∣ y } {\displaystyle \operatorname {E} \{x\mid y\}} .
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...