Twenty Nonparametric Statistics And Their Large Sample Approximations

Twenty Nonparametric Statistics And Their Large Sample Approximations

Linear Approximations for Functional Statistics in Large-sample Applications Linear Approximations for Functional Statistics in Large-sample Applications

We discuss methods for obtaining linear approximations to a functional statistic, with particular application to bootstrapping medium to large datasets. Existing methods use analytical approximations, nite-diierence derivatives, or linear regression using bootstrap results. Finite-diierence methods require an additional n evaluations of a functional statistic (where n is the numberof observatio...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Small sample approximations for spacing statistics

Edgeworth expansions as well as saddle-point methods are used to approximate the distributions of some spacing statistics for small to moderate sample sizes. By comparing with the exact values when available, it is shown that a particular form of Edgeworth expansion produces extremely good results even for fairly small sample sizes. However, this expansion suffers from negative tail probabiliti...

Sample Path Large Deviations for Order Statistics

We consider the sample paths of the order statistics of independent and identically distributed random variables with common distribution function F . If F is strictly increasing but possibly having discontinuities, we prove that the sample paths of the order statistics satisfy the large deviation principle in the Skorokhod M1 topology. Sanov’s theorem is deduced in the SkorokhodM ′ 1 topology ...