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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.
For example, the midhinge minus the median is a 3-term L-estimator that measures the skewness, and other differences of midsummaries give measures of asymmetry at different points in the tail. [1] Sample L-moments are L-estimators for the population L-moment, and have rather complex expressions. L-moments are generally treated separately; see ...
The conditional expectation of rainfall for an otherwise unspecified day known to be (conditional on being) in the month of March, is the average of daily rainfall over all 310 days of the ten–year period that fall in March. Similarly, the conditional expectation of rainfall conditional on days dated March 2 is the average of the rainfall ...
When the covariates are exogenous, the small-sample properties of the OLS estimator can be derived in a straightforward manner by calculating moments of the estimator conditional on X. When some of the covariates are endogenous so that instrumental variables estimation is implemented, simple expressions for the moments of the estimator cannot ...
For example, a triangular distribution might be used, depending on the application. In three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses: a = the best-case estimate; m = the most likely estimate; b = the worst-case estimate
In fact, it can be shown that the unconditional analysis of matched pair data results in an estimate of the odds ratio which is the square of the correct, conditional one. [2] In addition to tests based on logistic regression, several other tests existed before conditional logistic regression for matched data as shown in related tests. However ...
(The sample mean need not be a consistent estimator for any population mean, because no mean needs to exist for a heavy-tailed distribution.) A well-defined and robust statistic for the central tendency is the sample median, which is consistent and median-unbiased for the population median. The bootstrap distribution for Newcomb's data appears ...
An example application of the method of moments is to estimate polynomial probability density distributions. In this case, an approximating polynomial of order is defined on an interval [,]. The method of moments then yields a system of equations, whose solution involves the inversion of a Hankel matrix. [2]