|
In statistics, an ancillary statistic is a statistic whose sampling distribution does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to construct prediction intervals. This concept was introduced by the statistical geneticist Sir Ronald Fisher. ==Example== Suppose ''X''1, ..., ''X''''n'' are independent and identically distributed, and are normally distributed with unknown expected value ''μ'' and known variance 1. Let : be the sample mean. The following statistical measures of dispersion of the sample *Range: max(''X''1, ..., ''X''''n'') − min(''X''1, ..., ''Xn'') *Interquartile range: ''Q''3 − ''Q''1 *Sample variance: :: are all ''ancillary statistics'', because their sampling distributions do not change as ''μ'' changes. Computationally, this is because in the formulas, the ''μ'' terms cancel – adding a constant number to a distribution (and all samples) changes its sample maximum and minimum by the same amount, so it does not change their difference, and likewise for others: these measures of dispersion do not depend on location. Conversely, given i.i.d. normal variables with known mean 1 and unknown variance ''σ''2, the sample mean is ''not'' an ancillary statistic of the variance, as the sampling distribution of the sample mean is ''N''(1, ''σ''2/''n''), which does depend on ''σ'' 2 – this measure of location (specifically, its standard error) depends on dispersion. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「ancillary statistic」の詳細全文を読む スポンサード リンク
|