Information Criteria in Model Selection for Mixing Processes

We present information criteria for statistical model evaluation problems for stochastic processes. The emphasis is put on the use of the asymptotic expansion of the distribution of an estimator based on the conditional Kullback–Leibler divergence for stochastic processes. Asymptotic properties of information criteria and their improvement are discussed. An application to a diffusion process is presented.     

Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression

We study Beran's extension of the Kaplan-Meier estimator for thesituation of right censored observations at fixed covariate values. Thisestimator for the conditional distribution function at a given value of thecovariate involves smoothing with Gasser-Müller weights. We establishan almost sure asymptotic representation which provides a key tool forobtaining central limit results. To avoid complicated estimation ofasymptotic bias and variance parameters, we propose a resampling methodwhich takes the covariate information into account. An asymptoticrepresentation for the bootstrapped estimator is proved and the strongconsistency of the bootstrap approximation to the conditional distributionfunction is obtained.     

The use of historical control information in modelling dose response relationships in carcinogenesis

An empirical Bayes approach is proposed as a means of utilizing historical control information in modelling the relationship between the level of exposure to the test agent and the rate of tumour occurrence in carcinogenicity bioassays. Using a simple two-parameter linear logistic model, it is shown that when the historical control response rates are tightly clustered around the response rate in the concurrent control group, the empirical Bayes estimator can be considerably more precise than the usual maximum likelihood estimator ignoring the historical data. Efficiency gains were also noted with respect to estimates of quantiles of the dose response curve such as the ED₁₀. With a three-parameter logistic model in which spontaneously occurring lesions are assumed to be stochastically independent of those caused by the test agent, only modest gains in efficiency using historical control data were observed.     

门限自回归模型条件异方差的Kolmogorov-Smirnov检验

门限自回归模型被广泛地用于许多领域，当建立或使用这类模型时，一个重要问题是需要知道是否存在条件异方差。在本文中，我们对这个问题提出一个非参数检验，检验的大样本理论被给出，我们还通过数值模拟研究了检验方法的有限样本性质。结果表示检验有好的功效。经验百分位点还被给出。     

Testing Extreme Value Conditions

A test statistic is developed that checks the validity of the extreme value conditions without specifiying the shape parameter of the limiting extreme value distribution.     

Conditional tests for elliptical symmetry

In this paper, we suggest the conditional test procedures for testing elliptical symmetry of multivariate distribution. The conditional tests are exactly valid if the symmetric center and the shape matrix are given and are asymptotically valid if they are unknowns to be estimated. The equivalence, in the large sample sense, between the conditional tests and their unconditional counterparts is established. The power behavior of the tests under global as well as local alternatives is investigated theoretically. A small simulation study is performed.     

Effects of Mis-Specification in Bivariate Extreme Value Problems

The need to incorporate the structure of complex problems in extreme value analyzes, and the requirement to exploit all the limited information that is available, has led to the increased use of advanced dependence models. When they are appropriate, these dependence models can lead to substantial benefits over simpler univariate extreme value methods. Here we explore some inference problems for the marginal and conditional distributions caused by model mis-specification. We find distinct differences in estimation characteristics when the dependence structure is asymptotically dependent or asymptotically independent, and that conditional models can be substantially improved if the variables are standardized to have common marginal distributions.     

Approximation by randomly weighting method in censored regression model

Censored regression (“Tobit”) models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the performance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis. This work was supported by National Natural Science Foundation of China (Grant No. 10471136), PhD Program Foundation of the Ministry of Education of China, and Special Foundations of the Chinese Academy of Sciences and University of Science and Technology of China     

含附加信息时条件分位数的估计及其渐近性质

本文利用经验似然方法给出了含附加信息时条件分位数的一类新估计,在一定的正则条件下证明了估计的渐近正态性且渐近方差小于或等于通常的条件分位数核估计的渐近方差．     

Bootstrap tests in correspondence analysis

A bootstrap test is developed for testing models specified by Goodman in 1985 and 1986 for the correspondence analysis of two-way contingency tables. It enables testing goodness-of-fit in relation with the usual matrix decomposition method. An approximate table of critical values for the proposed test statistic is presented. Bootstrap confidence interval construction is also included. The behaviour of the test statistic and the confidence intervals is studied using Monte Carlo simulation.     

Interactive simulation of bushfires in heterogeneous fuels

The program IGNITE, developed by the authors, is a landscape fire modelling system that deals with fires in heterogeneous fuels. Landscapes are represented as cellular automata (grids of pixels) and fire spread is modelled as an epidemic process. An integrated geographic information system permits the importing and editing of maps from compatible sources, such as satellite imagery. Maps, models and other information are organized as scenarios; historical fires can be recorded and replayed. Modules are being developed for application to fire prevention, fire suppression, land-use management, and to training and education. An illustration of using the system to deal with heterogeneous fuel is its application to the problem of percolation in patchy fuel.     

Queue length estimation from probe vehicle location and the impacts of sample size

Probe vehicles are increasingly receiving more attention as an alternative means of collecting real-time traffic data needed for system optimization. This paper focuses on real-time estimation of queue lengths from the location information of probe vehicles in a queue at an isolated and undersaturated intersection. The paper also addresses the evaluation of the accuracy of such estimates as a function of the market penetration of probe vehicles. An analytical formulation based on conditional probability distributions is developed for estimating the expected queue length and its variance. It is found that, for the given settings, only the location information of the last probe vehicle in the queue is sufficient for the estimation. Exact expressions for the conditional mean and variance of queue length are derived. Various numerical results are documented to show how estimation errors behave by the volume to capacity ratio and by market penetration.     

Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models

Two tests for multivariate conditional heteroscedastic models are proposed. One is based on the cross-correlations of standardized squared residuals and the other is a score (Lagrange multiplier) test. The cross-correlations test can be used to detect the presence of multivariate conditional heteroscedasticity whereas the other test can be used for diagnostic checking. Simulation studies on the size and power of the test statistics are reported. The application of the tests is illustrated by an example using the S & P 500 and Sydney All Ordinary Indexes.     

A test of conditional heteroscedasticity in time series

A new test of conditional heteroscedasticity for time series is proposed. The new testing method is based on a goodness of fit type test statistics and a Cramer-von Mises type test statistic. The asymptotic properties of the new test statistic is establised. The results demonstrate that such a test is consistent. Project supported by the National Natural Science Foundation of China (Grant No. 19231050) and Postdoctoral Fund of China.     

Quasi-likelihood estimation of average treatment effects based on model information

In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.     

Effciency comparison between mean and log-rank tests for recurrent event time data

Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative effciency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that onl...     

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.     

Efficiency comparison between mean and log-rank tests for recurrent event time data

Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative efficiency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that only makes use of time to the first occurrence could be more efficient than the test for mean occurrence rates that makes use of all available recurrence times, provided that subject-to-subject variation of recurrence times is large. Explicit formula are derived for asymptotic relative efficiencies under the frailty model. The findings are demonstrated via extensive simulations. This work was supported by US National Science Foundation (Grant No. DMS-0504269)     

Uniform Asymptotic Expansion of Likelihood Ratio for Markov Dependent Observations

An asymptotic expansion of the logarithm of the likelihood ratio for Markov dependent observation is obtained. A functional limit theorem for the likelihood ratio is proved, which gives a way to study limiting distributions of the likelihood ratio based on stopping times, in particular, that of sequential probability ratio test.     

Testing heteroscedasticity by wavelets in a nonparametric regression model

In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.