On Rao score and PearsonX 2 statistics in generalized linear models

The identity of the Rao score and PearsonX ² statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results. Work financially supported by cofin. MIUR grants 2000 and 2002.     

On the equivalence of some test criteria based on BAN estimators for the multivariate exponential family

For the general multivariate exponential family of distributions it is shown that Rao's test criterion based on efficient scores is algebraically identical to the general chi-squared criterion based on maximum likelihood estimates and, similarly, that the Wald statistic is algebraically identical to the general minimum modified chi-squared statistic using linearization; these results are valid also for the multisample versions. Thus, these are extensions to the general exponential family of the findings due to Silvey (1970) and Bhapkar (1966), respectively, for the special case of the multinomial family.It is also shown that the general forms of the chi-squared and modified chi-squared criteria reduce to their respective well-known forms for the multivariate symmetric power series distribution. This finding is, thus, an extension of results noted by Ferguson (1958) and Clickner (1976) for the special case of the multinomial distribution.     

Hypotheses testing for a multidimensional parameter of inhomogeneous Poisson processes

We observe a realization of an inhomogeneous Poisson process whose intensity function depends on an unknown multidimensional parameter. We consider the asymptotic behaviour of the Rao score test for a simple null hypothesis against the multilateral alternative. By using the Edgeworth type expansion (under the null hypothesis) for a vector of stochastic integrals with respect to the Poisson process, we refine the (classic) threshold of the test (obtained by the central limit theorem), which improves the first type probability of error. The expansion allows us to describe the power of the test under the local alternative, i.e. a sequence of alternatives, which converge to the null hypothesis with a certain rate. The rates can be different for components of the parameter.     

An Empirical Analysis of Some Nonparametric Goodness-of-Fit Tests for Censored Data

In this article, we consider some nonparametric goodness-of-fit tests for right censored samples, viz., the modified Kolmogorov, Cramer–von Mises–Smirnov, Anderson–Darling, and Nikulin–Rao–Robson χ² tests. We also consider an approach based on a transformation of the original censored sample to a complete one and the subsequent application of classical goodness-of-fit tests to the pseudo-complete sample. We then compare these tests in terms of power in the case of Type II censored data along with the power of the Neyman–Pearson test, and draw some conclusions. Finally, we present an illustrative example.     

谈言微中,解颐解纷——饶少平先生的《杂体诗歌概论》论略

杂体诗作为中国文学遗产的一部分,其在文学史上的地位卑贱低下,一直引不起学者的重视。饶少平先生《杂体诗歌概论》的出版,填补了这方面研究的空白。其一方面吸纳了杂体诗的丰富之态与广博之趣,一方面又不失文学研究的宗旨,做到了＂辨章学术、考镜源流＂;同时,也使文学研究本身开始了有意义上的反顾与思考。     

Third-Order Asymptotic Distributions of Classic Test Statistics for One-Parameter Exponential Family Models

ABSTRACT

In this article we derive third-order asymptotic expansions for the non null distribution functions of four classic statistics under a sequence of local alternatives in one-parameter exponential family models. Our results are quite general and cover a wide range of important distributions.     

Variance bounds for estimators in autoregressive models with constraints

We consider nonlinear and heteroscedastic autoregressive models whose residuals are martingale increments with conditional distributions that fulfil certain constraints. We treat two classes of constraints: residuals depending on the past through some function of the past observations only, and residuals that are invariant under some finite group of transformations. We determine the efficient influence function for estimators of the autoregressive parameter in such models, calculate variance bounds, discuss information gains, and suggest how to construct efficient estimators. Without constraints, efficient estimators can be given by weighted least squares estimators. With the constraints considered here, efficient estimators are obtained differently, as one-step improvements of some initial estimator, similarly as in autoregressive models with independent increments.     

饶漱石与华东新区土地改革

1950-1952年,华东新区开展了土地改革运动。华东新区土改与北方老区土改相比显示出政策水平相对高一些的特点。在中共中央的指导下,中共中央华东局所采取的土改方针及处理地主阶级和与土地有关的工商业者的土地财产、保存富农经济、划分阶级成分、土改干部必须遵循的纪律、发展农业生产等方面的政策措施,是华东新区土改得以顺利推进和胜利结束的中心环节。当时,饶漱石担任中共中央华东局第一书记、华东军政委员会主席,华东新区土改是在他的领导下进行的。饶漱石在制定华东新区土改的方针政策措施和领导华东新区土改中做出了一定的贡献。饶漱石后来在“高饶反党联盟”事件中犯了严重的错误,中共中央对饶漱石所犯错误的处理是正确的,但饶漱石在领导华东新区土改中的贡献应该给予肯定。     

An Integral Bhattacharyya Type Bound for the Bayes Risk

In this article, some results are derived on stochastic comparisons of the residual and past lifetimes of an (n ? k + 1)-out-of-n system with dependent components. These findings generalize some recent results obtained on systems with independent components and provide some interesting results for a system with dependent components following an Archimedean copula. An illustrative example is provided.