Moments of the trace of a noncentral wishart matrix

Several articles have appeared on the moments of the trace of a noncentral Wishart matrix. Partial results are given in these papers but the representations of these partial results are often too cumbersome for any practical use. In this paper general results are given in compact form which are readily usable in practical problems.     

A further note on the bivariate normal distribution

It is indicated to what extent the conditional normality of the distribution of one comnonent of a bivariate random vector given the value of the other component together with a restricted type of conditional normality or the marginal normality for the other component is equivalent to the bivariate normality of this random vector.     

广义KDV-MKDV方程的精确解

利用直接积分方法将广义KDV-MKDV方程化为一阶变系数非线性常微分方程组,然后用待定系数法确定相应的常数获得了广义KDV-MKDV方程新的精确解;利用先作假设变换后选取试探函数的方法来直接构造广义KDV-MKDV方程新的精确解.     

Significance levels and confidence intervals for permutation tests

A computational algorithm is given which calculates exact significance levels of a wide class of permutation tests in the one and two sample problems. This class includes the permutation test based on the means, locally most powerful permutation tests and linear rank tests. When a shift model is assumed confidence intervals can also be obtained. Approximate methods, based on asymptotic expansions, are also presented.     

EXACT P‐VALUES FOR DISCRETE MODELS OBTAINED BY ESTIMATION AND MAXIMIZATION

In constructing exact tests from discrete data, one must deal with the possible dependence of the P‐value on nuisance parameter(s) ψ as well as the discreteness of the sample space. A classical but heavy‐handed approach is to maximize over ψ. We prove what has previously been understood informally, namely that maximization produces the unique and smallest possible P‐value subject to the ordering induced by the underlying test statistic and test validity. On the other hand, allowing for the worst case will be more attractive when the P‐value is less dependent on ψ. We investigate the extent to which estimating ψ under the null reduces this dependence. An approach somewhere between full maximization and estimation is partial maximization, with appropriate penalty, as introduced by Berger & Boos (1994, P values maximized over a confidence set for the nuisance parameter. J. Amer. Statist. Assoc. 89 , 1012–1016). It is argued that estimation followed by maximization is an attractive, but computationally more demanding, alternative to partial maximization. We illustrate the ideas on a range of low‐dimensional but important examples for which the alternative methods can be investigated completely numerically.     

A note on the moments of stochastic shrinkage parameters in ridge regression

The purpose of this note is to gain insight on the performance of two well known operational Ridge Regression estimators by deriving the moments of their stochastic shrinkage parameters. We also show that, under certain conditions, one of them has bounded moments.     

A note on the Edgeworth approximation to the distribution of Spearman's Rho with a correction to Pearson's approximation

The approximation of Edgeworth's form of the Gram-Charlier series to the exact cumulative distribution function (c.d.f.) of Spearman's Rank Correlation Coefficient is examined. For both the uncorrected and continuity correction cases, the maximum differences between the Edgeworth approximation and the exact c.d.f. is presented for 9 ≤ n ≤ 18. A correction to a similar, earlier table for the Pearson Type II approximation is also incorporated and comparisons made.     

杜甫研究应讲求谨严治学——为纪念杜甫逝世1230周年而作

杜甫研究在中国古代文学研究中堪称显学，一千二百年来杜甫研究成果的大量涌现，学术史的内容空前繁复与丰多，成就是主要的，缺憾也在所难免。本文就当前杜甫研究界的现状，提出杜甫研究中讲求谨严治学的必要性和迫切性。     

Distribution of the coates-diggle test statistic in case of replicated observations

A closed form expression for the distribution of a test statistic for comparing the spectral densities of stationary processes is given. This test statistic was introduced by COATES and DIGGLE ( 1986 ) for the unreplicated case and has been extended to the case of replicated observations by POTSCHER and RESCHENHOFER ( 1988 ). A simple method for computing approximate critical values in case of large numbers of replications is also provided. As a by-product an explicit expression for the distribution function of the range of independent variates each distributed as the logarithm of an F-variate i.e up to a factor of 2 each followin Fishers z-distriution is obtained     

Calculation of multidimensional stable densities

Stable random variables are used in economics, engineering, hydrology and physics to model situations where the underlying distributions are heavy tailed. Stable densities do not generally have explicit formula, even in one variable. This paper describes the steps necessary to calculate multivariate stable densities by numerically inverting the characteristic function. We give a program tocalculate two dimensional stable densites that uses a recent two dimensional adaptive quadratureroutine. Graphs of families of such densities are given for a range of values of a and various spectral measures