ECMT1010 Lecture Notes - Lecture 5: Statistic

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A bootstrapstatisticis to the original sample statistic as the o s s is to the population parameter. Recallthatthe sampling distribution is centered on the pp e thegolden rule implies thatthe bootstrapdistribution is centered on the samplestatistic. Recallthevariability of samplestatistics ismeasuredbythe s devofthesampling distribution sothegoldenrule implies the s devis e of the bootstrap distribution isusedtoestimatethevariabilityofthe sample statistic. Bootstrapping a s emaybeused toform a confidence intervalcc porportion p mean m difference in porportions lp pz difference in mean h ma. Aslong as the bootstrapdistribution is roughlysymmetricalwecan constructany confiden interval wewantby finding the appropriatepercentiles in the bootstrapdistribution. I lower bound obychangingpoloweshiftthe bounds ofthe f i ahigherpolo widerc i. For a polo confidence intervalwekeepthe middle polo ofbootstrapstatistics the middle polo definesthe upperandlower boundsof the p c i eg for 994a b i we keep99 leaving 0. 5 ateach tail. Method one estimate the s ebyfindingthestandarddeviation ofthebootstrap distribution then generate a 954 confidence intervalky statistic i 2 x s e.

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