We establish the Bahadur representation of sample quantiles for linear and some widely used nonlinear processes. Local fluctuations of empirical processes are discussed. Applications to the trimmed and Winsorized means are given. Our results extend previous ones by establishing sharper bounds under milder conditions and thus provide new insight into the theory of empirical processes for depende...

We establish the Bahadur representation of sample quantiles for linear and some widely used nonlinear processes. Local fluctuations of empirical processes are discussed. Applications to the trimmed and Winsorized means are given. Our results extend previous ones by establishing sharper bounds under milder conditions and thus provide new insight into the theory of empirical processes for depende...

For product manufacturing, control charts are important tools. Different types of control charts are used to monitor different measures of product characteristics. Among the numerous charts, the popular one is the Hotelling’s T 2 chart. It is designed while taking into account the most sensitive measures such as sample covariance matrix and sample mean vector. However, the chart becomes ineffec...

The auto-Poisson probability model furnishes an obvious tool for modeling counts of geographically distributed rare events. Unfortunately, its original specification can accommodate only negative spatial autocorrelation, which itself is a rare event. More recent alternative reformulations, namely, the Winsorized and spatial filter specifications, circumvent this drawback. A comparison of their ...

Let {(Xi,Yi)}i=1n be a sequence of independent bivariate random vectors. In this paper, we establish refined Cramér-type moderate deviation theorem for the general self-normalized sum ∑ i=1nXi/(∑i=1nYi2)1/2, which unifies and extends classical Cramér (Actual. Sci. Ind. 736 (1938) 5–23) theorems by Jing, Shao Wang (Ann. Probab. 31 (2003) 2167–2215) as well further version (J. Theoret. 24 (2011) ...

Abstract In the present study, we consider problem of missing and extreme values for estimation population variance. The presence either in study variable, or auxiliary both them, can adversely affect performance procedure. We three different situations also jackknife variance estimators by handling these under stratified random sampling. Bootstrap technique ABB is carried out to understand rel...

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust estimation/rescaling strategies in order to alleviate re...

Averaging (in statistical terms, estimation of the location of data) is one of the most commonly used procedures in neuroscience and the basic procedure for obtaining event-related potentials (ERP). Only the arithmetic mean is routinely used in the current practice of ERP research, though its sensitivity to outliers is well-known. Weighted averaging is sometimes used as a more robust procedure,...