Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions

Abstract.  We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.     

Generalized Maximum Spacing Estimation for Multivariate Observations

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbour balls are used as a multidimensional analogue to univariate spacings. A class of information‐type measures is used to generalize the concept of maximum spacing estimators. Weak and strong consistency of these generalized maximum spacing estimators are proved both when the assigned model class is correct and when the true density is not a member of the model class. An example of the generalized maximum spacing method in model validation context is discussed.     

Simple linear regression with multiple level shifts

The authors study the properties of the ordinary least squares trend estimator in a simple linear regression model with multiple known level shift times. The error component in the model is taken to be a general short‐memory stationary time series. The authors establish the consistency and asymptotic normality of the estimator. They also present a climatological application in which the multiple level shifts are prominent features.     

商业银行外部评级和资本市场评价比较研究

银行风险是当前中国面临的最主要的金融风险。为了准确评价银行的风险,首先介绍了两种最主要的方法——外部评级法和资本市场评价模型,再用默顿和KMV的相关理论计算了资本市场评价模型中最主要的参数d2,并用聚类的方法将d2分类后和外部评级法的结果进行比较,结果表明,市场评价模型的客观性和公正性较好,外部评级法的稳定性较好,两种方法各有优劣,可以互相借鉴。     

《家诫》和《颜氏家训》对儒家思想的相合与游离

嵇康和颜之推都服膺儒家教化，又分别出现游离于儒家的道家与佛家思想，他们的家训文《家诫》与《颜氏家训》深刻地体现了两种思想的矛盾，从生平身世到文章创作对两者进行对比，反映了二人的思想观念仍是以儒家思想为主，游离的道家与佛家思想是时代的烙印所造成。     

Weighted Wilcoxon Estimators in Nonlinear Regression

In this paper, we consider the estimation of parameters of a general near regression model. An estimator that minimises the weighted Wilcoxon dispersion function is considered and its asymptotic properties established under mild regularity conditions similar to those used in least squares and least absolute deviations estimation. As in linear models, the procedure provides estimators that are robust and highly efficient. The estimates depend on the choice of a weight function and diagnostics which differentiate between nonlinear fits are provided along with appropriate benchmarks. The behavior of these estimates is discussed on a real data set. A simulation study verifies the robustness, efficiency and validity of these estimates over several error distributions including the normal and a family of contaminated normal distributions.     

An efficient method for the estimation of multivariate moving averge models

Durbin's (1959) efficient method for the estimation of univariate moving average models is generalized to the vector case. Strong consistency and asymptotic normality of the estimator is proved. A simulation experiment is performed to illustrate the behaviour of the method in finite samples.     

Estimation of probability of extinction of a multitype branchihg process

Maximoa likelihood estimation of the probability of ultimata extinction of a possibly age dependentaultitype branching process is studied when independent random samples from off spring distributions are available, In multitype daIton-fatson branching process     

A pilot Monte Carlo study of two sequential estimation procedures based on generalized U-statistics

Recently two sequential estimation procedures based on generalized U-statistics have appeared in the statistical literature [Williams and Sen (1973, 1974)]. One of these procedures concerns the multi-sample problem of estimating a vector of parameters when the total sample size is fixed. The other procedure concerns the multi-sample problem of constructing a confidence ellipsoid of bounded maximum width for a vector of parameters. To supplement the asymptotic theory discussed in these earlier papers, a Monte Carlo study investigating the efficiency of these procedures for moderate sample sizes would be useful. This paper describes a preliminary Monte Carlo study utilizing a small number of replications and performed to provide information for the design of a more extensive study.     

On the construction of nonparametric density function estimators using the bootstrap

The derivation of a new class of nonparametric density function estimators, the so-called bootstrap functional estimators (BFE's), is given. These estimators are shown to be strongly consistent under fairly nonrestrictive conditions. Some small-sample properties are discussed and a number of graphs are presented.