Prediction in Some Poisson Errors in Variables Models

Predictive distributions are developed and illustrated for prediction in some Poisson errors in variables models. Two different situations in which multiplicative treatment effects are appropriate are considered within the context of predicting counts of road accidents. Hierarchical prior structures are investigated, and numerical integration and Gibbs sampling routines are used to derive the predictive and posterior probabilities. Examples of analyses are provided with data from road accidents in Sweden.     

An Asymptotic Analysis of the Logrank Test

Asymptotic expansions for the null distribution of the logrank statistic and its distribution under local proportional hazards alternatives are developed in the case of iid observations. The results, which are derived from the work of Gu (1992) and Taniguchi (1992), are easy to interpret, and provide some theoretical justification for many behavioral characteristics of the logrank test that have been previously observed in simulation studies. We focus primarily upon (i) the inadequacy of the usual normal approximation under treatment group imbalance; and, (ii) the effects of treatment group imbalance on power and sample size calculations. A simple transformation of the logrank statistic is also derived based on results in Konishi (1991) and is found to substantially improve the standard normal approximation to its distribution under the null hypothesis of no survival difference when there is treatment group imbalance. This revised version was published online in July 2006 with corrections to the Cover Date.     

英文写作错误中的社会和认知因素

许多从事二语写作教学研究的学者曾就学生写作中的句法错误、语篇错误及其它一些层面上的错误作过分析研究,然而对写作质量起着决定性作用的和二语习得相关的社会认知因素却少有提及。从社会和认知角度来探讨英文写作错误,这对于提高英文写作教学质量和学生写作水平将大有裨益。     

Testing parameter of the power series distribution of a zero inflated power series model

The Zero Inflated Power Series Distribution (ZIPSD) contains two parameters. The first parameter indicates inflation of zero and the other parameter is that of the Power Series distribution. We provide three asymptotic tests for testing the parameter of Power Series distribution, using an unconditional (standard) likelihood approach, a conditional likelihood approach and a test based on sample mean, respectively. The performance of these three tests has been studied for Zero Inflated Poisson Distribution (ZIPD). Asymptotic Confidence Intervals for the parameter are also provided.     

On testing random effects in the nested-error regression model

We derive an exact F-test for random effects in the nested-error regression model. The derivation utilizes a matrix decomposition that offers a transformation of the response vector into two independent subvectors. When the random effects are absent, the test statistic reduces to a ratio of two independent residual sums of squares that are computed by fitting a regression model using each subvector. A small simulation study compares the power of the F-test with various recent tests and shows that the proposed test has a competitive performance under small as well as large number of clusters.     

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.     

Estimating nonlinear additive models with nonstationarities and correlated errors

In this paper, we study a nonparametric additive regression model suitable for a wide range of time series applications. Our model includes a periodic component, a deterministic time trend, various component functions of stochastic explanatory variables, and an AR(p) error process that accounts for serial correlation in the regression error. We propose an estimation procedure for the nonparametric component functions and the parameters of the error process based on smooth backfitting and quasimaximum likelihood methods. Our theory establishes convergence rates and the asymptotic normality of our estimators. Moreover, we are able to derive an oracle‐type result for the estimators of the AR parameters: Under fairly mild conditions, the limiting distribution of our parameter estimators is the same as when the nonparametric component functions are known. Finally, we illustrate our estimation procedure by applying it to a sample of climate and ozone data collected on the Antarctic Peninsula.     

Tail asymptotic of discounted aggregate claims with compound dependence under risky investment

This paper considers the tail asymptotic of discounted aggregate claims with compound dependence under risky investment. The price of risky investment is modeled by a geometric Lévy process, while claims are modeled by a one-sided linear process whose innovations further obeying a so-called upper tail asymptotic independence. When the innovations are heavy tailed, we derive some uniform asymptotic formulas. The results show that the linear dependence has significant impact on the tail asymptotic of discounted aggregate claims but the upper tail asymptotic independence is negligible.     

Expansion and estimation of Lévy process functionals in nonlinear and nonstationary time series regression

In this article, we develop a series estimation method for unknown time-inhomogeneous functionals of Lévy processes involved in econometric time series models. To obtain an asymptotic distribution for the proposed estimators, we establish a general asymptotic theory for partial sums of bivariate functionals of time and nonstationary variables. These results show that the proposed estimators in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Finite sample simulations are provided to evaluate the finite sample performance of the proposed model and estimation method.