Local asymptotic normality for progressively censored likelihood ratio statistics and applications

Asymptotic Properties of Bootstrap Likelihood Ratio Statistics for Time Censored Data

Much research has been done on the asymptotic distributions of likelihood ratio statistics for complete data. In this paper we consider the situation in which the data are censored and the distribution of the likelihood ratio statistic is a mixture of continuous and discrete distributions. We show that the distribution of signed square root likelihood ratio statistic can be approximated by its ...

Asymptotic Normality of Graph Statistics

Various types of graph statistics for Bernoulli graphs are represented as numerators of incomplete U-statistics. Asymptotic normality of these statistics is proved for Bernoulli graphs in which the edge probability is constant. In addition it is shown that subgraph counts asymptotically are linear functions of the number of edges in the graph. AMS Subject Classification: Primary 05C99; Secondar...

An Empirical Likelihood Ratio Test for Normality

The empirical likelihood ratio (ELR) test for the problem of testing for normality is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are provided and analyzed using the Monte Carlo simulation technique. The power comparisons against a wide range of alternative distributions show that the ELR test is the most powerful of these tests in certain s...

Asymptotic normality of the maximum likelihood

We present conditions to obtain the asymptotic normality of the maximum likelihood estimator of a loss process presented in [2]. We shall use the notations of [2], write ‖ · ‖q for the standard L norm on an arbitrary space R, d ≥ 1, and let D φ denote the k−th order di erentiation with respect to φ. Let us introduce the following hypotheses: (A4) For all i ∈ {1, . . . , r}, λi(Φ0) > 0. (A5) For...

Generalized Likelihood Ratio Statistics