沈从文文学观念简评

本文对沈从文文学观念的几个方面,即"生命"美学观、"文学自由"论和文学功利观作了简要概括,并在现代文学理论史的背景上对其文学观念进行了一定的评价。在此基础上分析指出沈从文的文学观念同"改造民族灵魂"的基本文学观念的一致性,以及在"湘西价值"坚守下的独特性,从中探索沈从文对现代文学理论创作的启发意义和深远影响。     

Linear Subspace Spanned by Principal Points of a Mixture of Spherically Symmetric Distributions

For each positive integer k, a set of k-principal points of a distribution is the set of k points that optimally represent the distribution in terms of mean squared distance. However, explicit form of k-principal points is often difficult to obtain. Hence a theorem established by Tarpey et al. (1995 Tarpey , T. , Li , L. , Flury , B. D. ( 1995 ). Principal points and self-consistent points of elliptical distributions . Ann. Statist. 23 : 102 – 112 .[Crossref], [Web of Science ®] , [Google Scholar]) has been influential in the literature, which states that when the distribution is elliptically symmetric, any set of k-principal points is in the linear subspace spanned by some principal eigenvectors of the covariance matrix. This theorem is called a “principal subspace theorem”. Recently, Yamamoto and Shinozaki (2000b Yamamoto , W. , Shinozaki , N. ( 2000b ). Two principal points for multivariate location mixtures of spherically symmetric distributions . J. Japan Statist. Soc. 30 : 53 – 63 .[Crossref] , [Google Scholar]) derived a principal subspace theorem for 2-principal points of a location mixture of spherically symmetric distributions. In their article, the ratio of mixture was set to be equal. This article derives a further result by considering a location mixture with unequal mixture ratio.     

On the sample breakdown robustness of some nonparametric tests

In this paper, relying on the sample breakdown points, we investigate the sample breakdown properties of some nonparametric tests. It is shown that the sample breakdown points of the sign test asymptotically dominate those of the Wilcoxon test for one–sided hypotheses, However, the different conclusion is derived in the case of testing some shrinking neighborhood hypotheses. The breakdown behaviors of the Kolmogorov test and X²–test are also explored. These studies unify or refine some existing breakdown analyses of tests.     

Smoothing techniques via the bezier curve

Although the Bezier curve is very popular in the area of computational graphics it has rarely been used by statisticians. In this paper we develop methods and techniques for use of the Bezier curve in estimation of density and regression function. Also, asymptotic mean integrated square error for both estimators are derived. Comparisons with kernel estimator are conducted using simulation.     

Charts for finding upper percentage points of Student's t in the range .01 to .00001

The Bonferroni t-statistic is a versatile tool in multiple comparisons problems. The need for "oddball percentage points" may lead to extensive tables or heavy computation. Charts of t_p as a function of log p enable near two-decimal accuracy for any percentage point between .01 and .00001     

Correlation-Type Goodness of Fit Test for Extreme Value Distribution Based on Simultaneous Closeness

In reliability studies, one typically would assume a lifetime distribution for the units under study and then carry out the required analysis. One popular choice for the lifetime distribution is the family of two-parameter Weibull distributions (with scale and shape parameters) which, through a logarithmic transformation, can be transformed to the family of two-parameter extreme value distributions (with location and scale parameters). In carrying out a parametric analysis of this type, it is highly desirable to be able to test the validity of such a model assumption. A basic tool that is useful for this purpose is a quantile–quantile (QQ) plot, but in its use, the issue of the choice of plotting position arises. Here, by adopting the optimal plotting points based on Pitman closeness criterion proposed recently by Balakrishnan et al. (2010b Balakrishnan , N. , Davies , K. F. , Keating , J. P. , Mason , R. L. ( 2010b ). Computation of optimal plotting points based on Pitman Closeness with an application to goodness of fit for location-scale families. Submitted to Computational Statistics & Data Analysis.  [Google Scholar]), and referred to as simultaneous closeness probability (SCP) plotting points, we propose a correlation-type goodness of fit test for the extreme value distribution. We compute the SCP plotting points for various sample sizes and use them to determine the mean, standard deviation and critical values for the proposed correlation-type test statistic. Using these critical values, we carry out a power study, similar to the one carried out by Kinnison (1989 Kinnison , R. ( 1989 ). Correlation coefficient goodness of fit test for extreme value distribution . The American Statistician 43 : 98 – 100 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), through which we demonstrate that the use of SCP plotting points results in better power than with the use of mean ranks as plotting points and nearly the same power as with the use of median ranks. We then demonstrate the use of the SCP plotting points and the associated correlation-type test for Weibull analysis with an illustrative example. Finally, for the sake of comparison, we also adapt two statistics proposed by Gan and Koehler (1990 Gan , F. F. , Koehler , K. J. ( 1990 ). Goodness of fit based on P-P probability plots . Technometrics 32 : 289 – 303 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), in the context of probability–probability (PP) plots, based on SCP plotting points and compare their performance to those based on mean ranks. The empirical study also reveals that the tests from the QQ plot have better power than those from the PP plot.     

Further Results on Order Statistics Generated by Two Simulation Methods

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics.