Asymptotic distribution of regression correlation coefficient for Poisson regression model

This study treats an asymptotic distribution for measures of predictive power for generalized linear models (GLMs). We focus on the regression correlation coefficient (RCC) that is one of the measures of predictive power. The RCC, proposed by Zheng and Agresti is a population value and a generalization of the population value for the coefficient of determination. Therefore, the RCC is easy to interpret and familiar. Recently, Takahashi and Kurosawa provided an explicit form of the RCC and proposed a new RCC estimator for a Poisson regression model. They also showed the validity of the new estimator compared with other estimators. This study discusses the new statistical properties of the RCC for the Poisson regression model. Furthermore, we show an asymptotic normality of the RCC estimator.     

Surveillance of the interaction parameter of the ising model

Surveillance to detect changes of spatial patterns is of interest in many areas such as environmental control and regional analysis. Here the interaction parameter of the Ising model, is considered. A minimal sufficient statistic and its asymptotic distribution are used. It is demonstrated that the convergence to normal, distribution is rapid. The main result is that when the lattice is large, all approximations are better in several respects. It is shown that, for large lattice sizes, earlier results on surveillance of a normally distributed random variable can be used in cases of most interest. The expected delay of alarm at a fixed level of false alarm probability is examined for some examples.     

A powerful test for uniformity to detect highly peaked alternativedensities

A new class of statistical tests for uniformity based on sample ranges is proposed to detect a uniform density contaminated by a density with one or more high peaks. These kinds of alternatives occur quite frequently, especially in physics. It is shown that the proposed tests arc consistent and have high Pitman asymptotic relative efficiencies. Results of a Monte Carlo power study indicate that they, compared with other tests of uniformity, possess good power properties.A comparative study of various tests is also conducted using real data. An effcient algorithm for computing out test statistic and a table of percentage points are given, providing a practical guide for using the new test.     

Extreme statistics from the cosine distribution

The cosine distribution serves as a very good teaching example for which exact moment properties of extreme order statistics can be expressed in terms of elementary functions. This article presents the limiting joint distribution of the extreme order statistics for the cosine distribution. It is shown that burrows'(1986) result is a special case of the result presented in this article.     

EGARCH Model with Weighted Liquidity

We analyze a variant of the EGARCH model which captures the variation of the intra-day price. We study the asymptotic behavior of the estimators for the parameters of the model. We also illustrate our theoretical results by empirical studies.     

Inference in Targeted Group‐Sequential Covariate‐Adjusted Randomized Clinical Trials

This article is devoted to the construction and asymptotic study of adaptive, group‐sequential, covariate‐adjusted randomized clinical trials analysed through the prism of the semiparametric methodology of targeted maximum likelihood estimation. We show how to build, as the data accrue group‐sequentially, a sampling design that targets a user‐supplied optimal covariate‐adjusted design. We also show how to carry out sound statistical inference based on such an adaptive sampling scheme (therefore extending some results known in the independent and identically distributed setting only so far), and how group‐sequential testing applies on top of it. The procedure is robust (i.e. consistent even if the working model is mis‐specified). A simulation study confirms the theoretical results and validates the conjecture that the procedure may also be efficient.     

HAZARD RATE ESTIMATION FOR CENSORED DATA BY WAVELET METHODS

ABSTRACT

We study the estimation of a hazard rate function based on censored data by non-linear wavelet method. We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based hazard rate estimators under randomly censored data. We show this MISE formula, when the underlying hazard rate function and censoring distribution function are only piecewise smooth, has the same expansion as analogous kernel estimators, a feature not available for the kernel estimators. In addition, we establish an asymptotic normality of the nonlinear wavelet estimator.     

On the asymptotic distribution of cramer-von mises one-sample test statistics under an alternative

The asymptotic normality of the Cramer-von Mises one-sample test statistic and one of its variants under an alternative cdf is demonstrated. The derivation herein is unique in that it does not require knowledge of the theory of weak convergence of probability measures defined on metrized function spaces, and thus is accessible to a broader class of students and practitioners.     

An Orthogonality‐Based Estimation of Moments for Linear Mixed Models

Abstract. Estimating higher‐order moments, particularly fourth‐order moments in linear mixed models is an important, but difficult issue. In this article, an orthogonality‐based estimation of moments is proposed. Under only moment conditions, this method can easily be used to estimate the model parameters and moments, particularly those of higher order than the second order, and in the estimators the random effects and errors do not affect each other. The asymptotic normality of all the estimators is provided. Moreover, the method is readily extended to handle non‐linear, semiparametric and non‐linear models. A simulation study is carried out to examine the performance of the new method.