Bootstrapping multivariate UU-quantiles and related statistics

AbstractThe asymptotic consistency of the bootstrap approximation of the vector of the marginal generalized quantiles of U-statistic structure (multivariate U-quantiles for short) is established. The asymptotic accuracy of the bootstrap approximation is also obtained. Extensions to smooth functions of marginal generalized quantiles are given and some specific examples, such as the vector of marginal sample quantiles and the vector of marginal Hodges-Lehmann location estimators, are discussed

On a crossroad of resampling plans : bootstrapping elementary symmetric polynomials

We investigate the validity of the bootstrap method for the elementary symmetric polynomials S_n^{(k)={nchoose k^{-1sumsb {1leq i_1 < ...< i_k leq n X_{i_1...X_{i_k of i.i.d. random variables $X_1,dots,X_n$. For both fixed and increasing order $k$, as $ntoinfty$ the cases where mu= {rm E X_1 neq0, the nondegenerate case, and where mu= {rm E X_1=0, the degenerate case, are considered

Limit theorems for rank statistics

The purpose of the paper is to extend the weak asymptotic results for the weighted partial sums of i.i.d. random variables to the weighted partial sums of rank scores. These results then suggest various test procedures for the change point problem. The crucial tools in the proofs are martingale property of a class of two-sample rank statistics and the Hájek results (1961) of the simple linear rank statistics.Rank statistics Weighted maxima Location model

Omnibus tests for the error distribution in the linear regression model

Test procedures are constructed for testing the goodness-of-fit of the error distribution in the regression context. The test statistic is based on an L2-type distance between the characteristic function of the (assumed) error distribution and the empirical characteristic function of the residuals. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated, while the issue of the choice of suitable estimators has been particularly emphasized. Theoretical results are accompanied by a simulation study

Serial rank statistics for detection of changes

A class of ranks based test statistics for testing hypothesis of randomness (observations are independent and identically distributed) against the alternative that the observations become dependent at some unknown time point is introduced and its limit properties are studied. The considered problem belongs to the area of the change-point analysis.Independence AR-sequences Change point detection Serial rank statistics