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针对特定备择设计的拟合优度检验AI 解读

SUMMARY We examine a large class of distributional tests equivalent to tests based on degenerate U-statistics. The factors which influence the performance of these tests are isolated. An analysis of the factors leads us to suggest tests with improved power properties against certain types of alternatives. One such test is based on a chi squared statistic which employs overlapping cells, rather than disjoint cells. It is shown that this test has power superior to that of the…

非线性回归中渐近分布的适用性与曲率AI 解读

SUMMARY In a non-linear regression model, correction terms for the asymptotic distribution of the maximum likelihood estimator are found. They can all be evaluated by the parameter dependent part of Beale's (1960) measure of non-linearity and some of the terms can be evaluated by Bates and Watts (1980) parameter dependent curvature in specific directions. The theory is illustrated by examples.

线性回归误差协方差矩阵的局部最优不变检验AI 解读

SUMMARY This paper considers a class of hypothesis testing problems concerning the covariance matrix of the disturbances in the classical linear regression model. A test that is locally best invariant against one-sided alternative hypotheses is constructed and shown to be identical to a one-sided version of the Lagrange Multiplier test.

总体间异质性的分析AI 解读

SUMMARY A set of populations, each of which is characterized by a distribution, is said to be “overall homogeneous” if the underlying distributions are identical. Assuming that the underlying distributions are normal or multinomial, this paper provides a theory of establishing test statistics for testing hypotheses of homogeneity within subsets of populations and of homogeneity between subsets of populations. The desired test statistics are derived by a decomposition of the…

有限混合模型中的估计与假设检验AI 解读

SUMMARY Finite mixture models are a useful class of models for application to data. When sample sizes are not large and the number of underlying densities is in question, likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter, λ, and the parameter of the underlying densities, θ, are problematical. Our approach places a prior distribution on λ and estimates θ by maximizing the likelihood of the data given θ with λ integrated out.…

可微统计泛函的刀切法AI 解读

SUMMARY The purpose of this paper is to give a general unified view of “how smooth” a statistic needs to be for the jackknife to work. We give general sufficient conditions for the jackknife to produce consistent bias and variance estimators, and for linear combinations of the pseudovalues to be asymptotically normal. Regularity conditions are stated in terms of the existence of strong Fréchet differentials of the functional version of the statistic being jackknifed.

替代异常值模型下限制最大似然估计的一则札记AI 解读

SUMMARY For single outliers in normal theory fixed effects models a mean slippage model is commonly used. An alternative is to model the outlier as arising from an unknown observation with inflated variance. Maximum likelihood estimates for the position of the outlier under the two models need not agree. This paper considers maximizing a restricted part of the likelihood to estimate the variance parameters and characterizes these estimates in terms of standard least squares…

非参数回归曲线拟合中样条平滑方法的若干方面AI 解读

SUMMARY Non-parametric regression using cubic splines is an attractive, flexible and widely-applicable approach to curve estimation. Although the basic idea was formulated many years ago, the method is not as widely known or adopted as perhaps it should be. The topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology. Particular subjects covered include the basic principles of the…

存在干扰参数时置信限的渐近展开及应用AI 解读

SUMMARY Series expansions for confidence limits based on consistent estimators are obtained in the presence of nuisance parameters. The maximum likelihood estimator is treated as a special case and the necessary characteristics of its sampling distribution are obtained in terms of basic quantities derivable from the likelihood function. The theory is applied to the problem of setting separate confidence limits for the scale and shape parameters of the Weibull distribution.…

极限密度函数的渐近正态性及其贝叶斯含义AI 解读

SUMMARY Precise statements of three basic conditions for the asymptotic normality of limiting density functions are given. In the Bayesian context, these conditions as a whole provide a greater generality and more operational flexibility for asymptotic posterior normality than those assumed by previous investigators.

带顺序约束的分类数据模型中有限总体参数的贝叶斯估计AI 解读

SUMMARY This note describes a Bayesian method for estimation of finite population parameters in general population surveys where acceptable regression-type models are typically unavailable. A categorical data model is adopted as in Ericson (1969, Section 4). However, specifications of smoothness are incorporated into the prior distribution. These smoothness conditions are expressed as unimodal or, possibly, multi-modal order relations among the category probabilities.…

关于多项式函数关系模型AI 解读

SUMMARY A method for obtaining consistent estimators of the coefficients in a polynomial functional relationship model with normal errors is proposed when the error covariance matrix is either completely known or known up to a proportionality factor. For quadratic functional relationships with possibly non-normal errors, we present a consistent estimator when the error covariance matrix is known. A large sample test of the quadratic against the linear functional relationship…

位置线性判别函数的渐近分布AI 解读

SUMMARY The location linear discriminant function forms the basis of the optimal Bayes classification rule when the data contain both binary and continuous variables (Krzanowski, 1975). When the unknown parameters are replaced by their sample estimates, the resulting “estimative” rule has an exact distribution which is too complicated for numerical use. We present here an asymptotic expansion of this distribution and study its performance under various assumptions about the…

关于球面样条的一个注记AI 解读

SUMMARY This paper presents two families of curves for interpolating and smoothing sequences of points on the surface of the unit sphere. One family is a natural analogue of the usual splines for curve-fitting in the plane; the other is slightly less optimal but more convenient from a computational viewpoint.

逆高斯变量的精确卡方分解定理AI 解读

SUMMARY It is proved that the scaled deviance of an inverse Gaussian sample of size n can be expressed as a sum of n – 1 independent chi-square variates. Applications to prediction intervals and squared recursive-residuals are illustrated.

临床试验两阶段程序的极小极大风险AI 解读

SUMMARY The risk involved in a trial to compare two medical treatments is shared by patients who receive the inferior treatment during the experimental phase and those remaining after the experiment who might all receive the inferior treatment if the results are misleading. We consider the maximum of this risk with respect to the unknown probabilities of success and seek allocation rules that minimize this quantity, for a given total of patients. It needs extensive…

正依赖对分类数据卡方检验的影响AI 解读

SUMMARY We introduce a general definition of positive dependence for finite-state processes, and show that if successive observations are positively dependent, all tests that are asymptotically equivalent to standard Pearson chi-squared tests have asymptotic null distributions stochastically larger than those obtained under the usual independence assumptions. Ignoring positive dependence therefore leads to too frequent rejection of null hypotheses. This qualitative…

存在缺失观测时的回归序列相关检验AI 解读

SUMMARY In order to test for serial correlation in residuals for static time series regression in the presence of missing data, the score principle is applied both to the likelihood conditional on the observation times, and to an unconditional form of likelihood. Asymptotic distributions of the test statistics are established, under both the null hypothesis of no serial correlation, and sequences of local, correlated, alternatives, enabling analytic comparison of efficiency.

一种高阶马尔可夫链模型AI 解读

SUMMARY A model for Markov chains of order higher than one is introduced which involves only one additional parameter for each extra lag. Asymptotic properties and the autocorrelation structure are investigated. Three examples are given in which the model appears to model data more successfully than both the usual high-order Markov chain and the alternative models of Jacobs and Lewis (1978), Pegram (1980) and Logan (1981).

计算机通信系统的随机模型AI 解读

SUMMARY This paper describes some examples of the stochastic models found useful in the design and analysis of advanced computer and communication systems. Our major theme might be termed the control of contention. As illustrations of this theme we discuss concurrency control procedures for databases, dynamic channel assignment for cellular radio, and random access schemes for the control of a broadcast channel. We emphasize asymptotic properties of product-form…

多元正态情形下广义中位数的渐近性质AI 解读

SUMMARY The generalized affine invariant median proposed by Oja (1983) is, in the case of multivariate normality, shown to be asymptotically at least as efficient as the spatial median.

倒数矩的界及其在 Stein 估计与后分层中的应用AI 解读

SUMMARY Bounds on the kth reciprocal moment of a distribution are given in terms of the mean, variance and left extremity of the distribution. A methodology for obtaining distribution-specific bounds, with improved accuracy, is outlined. Some natural approximations are noted. Applications are given in Stein estimation, and in classical and Bayesian post-stratification.

平滑样条的诊断方法AI 解读

SUMMARY Diagnostic measures appropriate for use with smoothing splines are derived and their properties are investigated. The proposed measures focus on detection of observations which substantially influence the fit and provide additional information over that obtained from examination of residuals alone. A numerical example illustrates the technique.

多参数线性化定理AI 解读

SUMMARY A linearization theorem represents an estimating equation for an unknown parameter as approximately linear in the neighbourhood of the true parameter point, and can provide a convenient approach to asymptotic theory. A multiparameter version of a standard linearization theorem is proved, and applied to two examples: M-estimates in multiple regression, and the spherical median.