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基于估计函数的面板计数边际分析AI 解读

We develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations, using two types of self-consistent estimating equations. The first is derived from the likelihood studied in Wellner & Zhang (2000), assuming a Poisson counting process, and gives a nondecreasing estimator, which is the same as the nonparametric maximum likelihood estimator of Wellner & Zhang and thus is consistent without the Poisson…

利用 Gibbs 抽样获得条件检验及其应用AI 解读

A random sample is drawn from a distribution which admits a minimal sufficient statistic for the parameters. The Gibbs sampler is proposed to generate samples, called conditionally sufficient or co-sufficient samples, from the conditional distribution of the sample given its value of the sufficient statistic. The procedure is illustrated for the gamma distribution. Co-sufficient samples may be used to give exact tests of fit; for the gamma distribution these are compared for…

过度加重尾部权重会降低检验效率AI 解读

Test statistics which are almost determined by $o(n)$ tail order statistics are shown to provide tests of asymptotic relative efficiency 0 against the usual type of contiguous alternative. The result is applied to several goodness-of-fit tests: the variance weighted Kolmogorov-Smirnov statistic, the Kolmogorov-Smirnov statistic in the stabilized probability plot and the correlation coefficient in a $Q - Q$ plot for a variety of distributions with exponential tails.

大量区组设计中的正态误差检验AI 解读

Goodness-of-fit tests are provided for the assumption of homoscedastic normal errors in experimental designs where the number of fitted parameters is large. Asymptotic critical points are given for the Cramér-von Mises statistic, Watson's statistic and the Anderson-Darling statistic. An expansion of the covariance function of the empirical process of standardized residuals is given. The corresponding weak convergence result is established for one-way layouts when the number…

多区组设计中的正态误差检验AI 解读

Goodness-of-fit tests are provided for the assumption of homoscedastic normal errors in experimental designs where the number of fitted parameters is large. Asymptotic critical points are given for the Cramér-von Mises statistic, Watson's statistic and the Anderson-Darling statistic. An expansion of the covariance function of the empirical process of standardized residuals is given. The corresponding weak convergence result is established for one-way layouts when the number…

基于标准化间距的拟合优度检验AI 解读

SUMMARY Normalized spacings provide useful tests of fit for many suitably regular continuous distributions; attractive features of the tests are that they can be used with unknown parameters and also with samples which are censored (Type 2) on the left and/or right. A transformation of the spacings leads, under the null hypothesis, to a set of z-values in (0, 1); however, these are not uniformly distributed except for spacings from the exponential or uniform distributions.…

冯·米塞斯分布的拟合检验AI 解读

Critical points for the asymptotic distribution of Watson's U2 statistic are given for testing the hypothesis that a sample comes from the two-parameter von Mises distribution on the circle when one or more of the parameters is unknown. Monte Carlo results show that convergence to the asymptotic distribution is quick. Dependence of the points on the shape parameter is discussed and seen not to cause any problems.