日期精度：到日 16 篇 · 到月 8 篇 · 到年 11 篇
von Mises–Fisher 分布的贝叶斯推断
The main aim of this note is to give a theoretical discussion of Bayesian inference for the von Mises-Fisher distribution. The choice of particular priors is considered and the admissibility of certain Bayesian estimators studied. For the multisample case estimators are given. Some problems of testing hypotheses are summarized in the form of posterior odds against the null hypothesis.
方向数据统计
Summary Directional data analysis is emerging as an important area of statistics. Within the past two decades, various new techniques have appeared, mostly to meet the needs of scientific workers dealing with directional data. The paper first introduces the two basic models for the multi-dimensional case known as the von Mises–Fisher distribution and the Bingham distribution. Their sampling distribution theory depends heavily on the isotropic case and some developments are…
多峰与轴向圆周总体的多样本检验
Summary We propose an l-modal c-sample non-parametric test U on a circle based on uniform scores. The test is derived with the help of an l-modal von Mises type distribution. Critical values of the distribution are given and the asymptotic distribution of U and its parametric competitor V are obtained. For the shift-type alternatives we derive Bahadur's efficiency of the U-test relative to the V-test and consider some particular cases. We also examine the small sample powers…
圆周数据的多样本均匀得分检验及其参数竞争检验
Summary We propose a c-sample non-parametric test W on a circle based on uniform scores. The test can be regarded as an extension of Wheeler and Watson's test (1964). This test is constructed with the help of a variant of a c-sample test for von Mises populations under the shift-type of alternatives. We indicate the relationship of the W-test with a test given by Mardia (1970). This result solves the problem of critical values of this test and of approximations to the null…
二元多样本非参数检验
Summary A non-parametric test for the bivariate c-sample problem is proposed. The test is an extension of a bivariate two-sample test given by Mardia (1967) and possesses various desirable properties. We derive the asymptotic distribution of this test and obtain the Pitman efficiency of the test relative to Wilks's criterion A for the translation types of alternatives. We give the critical values of the distribution and some approximations. The test is applied to a numerical…
多元偏度与峰度度量及其应用
Measures of multivariate skewness and kurtosis are developed by extending certain studies on robustness of the t statistic. These measures are shown to possess desirable properties. The asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test of multivariate normality is proposed. The effect of nonnormality on the size of the one-sample Hotelling's T2 test is studied empirically with the help of these measures, and it…
双变量两样本非参数检验的零假设分布
Summary A non-parametric test criterion U for the bivariate two-sample problem has been proposed by Mardia (1967). It is shown in Mardia (1968) that a two-sample test on a circle proposed by Wheeler and Watson (1964) has the same null distribution as that of U. In view of this additional application, we extend the table of critical values of U given in Mardia (1967), give a new approximation to the null distribution and compare it with the approximations given in Mardia…
列联型二元分布下若干独立性检验的表现
Plackett (1965) has given a family of contingency-type bivariate distributions. We examine the Pitman efficiency of some tests of independence against alternatives of this kind. We find that the tests based on Spearman's rank correlation coefficient rs, Kendall's coefficient and on certain other measures are asymptotically equivalent. The asymptotic relative efficiency (ARE) of rS, relative to the ordinary correlation coefficient, is greater than or equal to 1. An example is…
正态情形下二维两样本位置非参数检验的小样本功效
Summary The exact power of a test U (Mardia, 1967) is obtained for normal location alternatives, but even for small samples the expression cannot be simplified. The empirical power function of the U-test is obtained and compared with the power of Hotelling's T2 by extending some efficiency measures and developing a new non-central T2 routine. It is found that the efficiency of the U-test relative to Hotelling's T2 test decreases with N and lies between 79 and 93 per cent.
Summary An unconditional non-parametric test for the bivariate two-sample problem is proposed. The test is shown to possess various desirable properties. We give critical values of the distribution, some approximations and its asymptotic distribution. For the shift type of alternative hypotheses, we show here that U is distributed asymptotically as a non-central chi-square. We have derived its Pitman's asymptotic efficiency relative to Hotelling's T 2 for these alternatives…
列联型二元分布的若干进展
Plackett (1965) has given a class of contingency-type bivariate distributions which contains the boundary distributions and the member corresponding to independent random variables. This is the only bivariate class known to possess this important property. In addition, Plackett (1965) has given some interesting applications of these distributions. The class is determined by solving a quadretic equation and discarding one of the roots not satisfying a set of inequalities. In…