The distribution of each member of the family of statistics based on the -divergence for testing goodness-of-fit is a chi-squared to (Pardo [pard96]). In this paper a closer approximation to the exact distribution is obtained by extracting the -dependent second order component from the term.
We propose a sequential monitoring scheme for detecting a change in scale. We consider a stable historical period of length . The goal is to propose a test with asymptotically small probability of false alarm and power 1 as the length of the historical period tends to infinity. The asymptotic distribution under the null hypothesis and consistency under the alternative hypothesis is derived. A small simulation study illustrates the finite sample performance of the monitoring scheme.
We consider a measure of the diversity of a population based on the λ-measure of hypoentropy introduced by Ferreri (1980). Our purpose is to study its asymptotic distribution for testing hypotheses. A numerical example based on real data is given.
A statistic using the concept of order - weighted information energy introduced by Tuteja et al. (1992) is considered and its asymptotic distribution in a stratified random sampling is obtained. Some special cases are also discussed.
New statistical procedures for a change in means problem within a very general panel data structure are proposed. Unlike classical inference tools used for the changepoint problem in the panel data framework, we allow for mutually dependent panels, unequal variances across the panels, and possibly an extremely short follow up period. Two competitive ratio type test statistics are introduced and their asymptotic properties are derived for a large number of available panels. The proposed tests are...