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删失观测、重复测量与混合效应模型：正态误差下的 EM 方法AI 解读

Maximum likelihood estimation of a vector regression parameter and variance com ponents is considered for the mixed effects model when observations are right censored. A general scheme of estimation is given using the EM algorithm and detailed results found for the model with between and within block variation. This model is applied to the logarithms of survival times from a repeated measures design.

非线性回归中的偏差AI 解读

We investigate the biases of the residuals and maximum likelihood parameter estimates from normal nonlinear regression models. Emphasis is placed on a class of partially nonlinear models, on the role of individual cases in determining bias, on how bias affects standard diagnostic methods, and on the relationship between bias and curvature.

基于分层样本的回归分析AI 解读

Jewell (1985) described an iterative method of estimating parameters in the linear regression model from data collected from stratified samples of the dependent variable with no parametric assumptions on the residual distribution. The present paper considers an alternative iterative technique which is generally superior in terms of efficiency, often by a considerable amount. The method is extended to cover stratified sampling on a design variable which is correlated with the…

利用调查数据估计分布函数AI 解读

A simple method for estimating population distribution functions and associated quantiles from sample survey data is described and some asymptotic theory for it presented. The method assumes a model-based approach to survey estimation and allows auxiliary population information to be directly incorporated into the estimation process. Monte Carlo results comparing the proposed method with conventional design-based methods are given. These suggest that the model-based approach…

过度离散计数与比例数据矩估计量的渐近性质AI 解读

Consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra-binomial and extra-Poisson variation. The asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter. The moment estimates may be obtained using iterated weighted least squares.

高效自助法模拟AI 解读

Bootstrap methods are simulation methods for assessing sampling properties of statistical estimates. We discuss two ideas for making the simulation more efficient. The first idea is to balance the simulated samples, and the second idea is to make explicit use approximations which do not require simulation. Both ideas are illustrated with three examples.

一种不等概率抽样方案AI 解读

A new sampling scheme, with probability of inclusion proportional to size, is proposed for a sample of given size n. It satisfies many requirements of a good sampling scheme under conditions usually met in practice. Empirical exploration of the feasibility of the proposed sampling scheme and of the stability of its variance, shows satisfactory performance.

关于逻辑回归最大似然估计存在条件的补充说明AI 解读

This note expands the paper by Albert & Anderson (1984) on the existence and uniqueness of maximum likelihood estimates in logistic regression models. Their three possible mutually exclusive data patterns: (i) overlap, (ii) complete separation, and (iii) quasiseparation are considered. The maximum likelihood estimate exists only in (i). Modifications of the statement and proofs of Albert & Anderson's results are given for (ii) and (iii) The identifiability for a more general…

误差模型类别下回归参数估计量方差的保守估计AI 解读

Robust estimates of precision are obtained for generalized least-squares regression parameter estimators. They are robust in the sense of being conservative estimates of the variances of the parameter estimators when the error model is imprecisely specified. Serially-structured errors are one possible class. Substantial amounts of computing are required in each application. A numerical example is given in which errors are independent but do not necessarily have equal…

关于似然比检验 Bartlett 调整的一则说明AI 解读

The invariance properties of the likelihood ratio statistic are used to question the validity of certain terms arising in the expansion of its null distribution. It is suggested that the null distribution of Bartlett adjusted tests is the appropriate reference chi-squared distribution with error of order n−3/2, where n is the sample size.

自回归移动平均模型的普通与似然型位置M估计AI 解读

Proper location M-estimates for a model with non-Gaussian autoregressive-moving average type errors are genuine maximum likelihood type estimates, whereas ordinary location M-estimates are those introduced by P. Huber for independent and identically distributed errors. The relative behaviour of ordinary location M-estimates and proper location M-estimates is studied for situations with dependent errors of purely autoregress ive and purely moving average type. It is shown…

非负回归系数零约束的联合检验AI 解读

Three tests for zero restrictions on regression coefficients that are known to be nonnegative\nare considered: the classical F test, the likelihood ratio test, and a one-sided t test\nin a particular direction. Critical values for the likelihood ratio test are given for the\ncases of two and three restrictions, and the power function is calculated for the case of\ntwo restrictions. The analysis is conducted in terms of a characterization of the clas\nall similar tests for…

非线性回归中的残差方差与残差模式AI 解读

A nonparametric estimator of residual variance in nonlinear regression is proposed. It is based on local linear fitting. Asymptotically the estimator has a small bias, but a larger variance compared with the parametric estimator in linear regression. Finite sample properties are investigated in a simulation study, including a comparison with other nonparametric estimators. The method is also useful for spotting heteroscedasticity and outliers in the residuals at an early…

允许高剂量响应下降的剂量反应关系递归非参数检验AI 解读

A general recursive strategy is introduced to test nonparametrically for an increasing dose-response relationship when a downturn in response at high doses is possible. A specific implementation involving a test of Jonckheere (1954) and Terpstra (1952) is considered, and its size and power properties are investigated via Monte Carlo methods. Data from mutation research illustrate the phenomenon of concern.

序贯检验后最大似然估计的偏差AI 解读

The bias of maximum likelihood estimates calculated at the end of a sequential procedure is investigated. For the two sequential designs considered in detail, the sequential probability ratio test and the triangular test, this bias is appreciable. A method of calculating an adjusted estimate with reduced bias is described, and an approximation to the standard error of the new estimate is provided. Examples of the implementation of the method are given, and its advantages and…

相似检验与标准化对数似然比统计量AI 解读

When testing an affine hypothesis in an exponential family the ‘ideal’ procedure is to calculate the exact similar test, or an approximation to this, based on the conditional distribution given the minimal sufficient statistic under the null hypothesis. By contrast to this there is a ‘primitive’ approach in which the marginal distribution of a test statistic considered and any nuisance parameter appearing in the test statistic is replaced by an estimate. We show here that…

椭圆伽马分布诱导的广义非中心卡方分布AI 解读

Certain important statistical inference and classification problems lead to the consideration of quadratic forms in rotationally invariant random variables. In this paper noncentral probabilities under a multivariate elliptical gamma distribution are studied. The density and cumulative distribution function of the squared noncentral radii are expressed in a Laguerre series form and certain recurrences are derived. Finally, two numerical approximations are discussed.

von Mises 分布平均方向的近似置信区间AI 解读

Simple formulae are suggested that provide accurate confidence bounds for the mean direction of a sample from a von Mises distribution. These formulae obviate the need for calculating an estimate of the second trigonometric moment, and dispense with nomograms.

逐次提高辅助统计量的辅助性阶数AI 解读

It is shown by an argument similar to one of Welch (1947) that it is, under usual regularity conditions, in general possible to improve the order of ancillarity successively. This means that when an asymptotic ancillary has been constructed, such that its distribution is independent of the parameter apart from terms of order Othen a new ancillary may be constructed with a distribution which depends on the parameter only through terms of order O. It is shown how the new…

有限总体系统抽样与分层抽样的若干渐近结果AI 解读

A sample mean has an asymptotically insignificant model bias under a broad set of functional relationships between the parameter of interest and an auxiliary size variable given a systematic sample from a size ordered list. When based on randomly drawn samples within size strata, this estimator of the population mean not only has an asymptotically insignificant model bias but is design consistent as well. In addition, there are more efficient estimation strategies that have…

参数经估计的状态空间模型预测均方误差AI 解读

We obtain a conditional prediction mean squared error for a state space model with estimated parameters. An important application of our results is the derivation of conditional forecast and interpolation mean squared errors for autoregressive-moving average models with estimated parameters. We also obtain the conditional mean squared error for filtered and smoothed estimates of the state vector.

二项随机变量对数的偏差与高阶累积量AI 解读

The bias and first four cumulants of the distribution of the logarithm of a binomial variate are studied by means of asymptotic expansions and exact computation. A new estimator of the variance is derived and evaluated. The asymptotic skewness is found to differ from the result of Walter (1975). Applications to point estimation of the one-hit curve and the interval estimation and testing of the ratio of binomial parameters are considered. Because of the bias and nonnormality…

广义线性模型的最优有界得分函数及其在逻辑回归中的应用AI 解读

We study optimally bounded score functions for estimating regression parameters in a generalized linear model. Our work extends results obtained by Krasker & Welsch (1982) for the linear model and provides a simple proof of Krasker & Welsch's first-order condition for strong optimality. The application of these results to logistic regression is studied in some detail with an example given comparing the bounded-influence estimator with maximum likelihood.

判别问题的似然方法AI 解读

Suppose independent observations are drawn such that k have a known density g(x) and n – k have a known density f(x). We consider the discrimination problem of allocating observations to their parent densities. The rule minimizing the expected number of misclassifications is written as a function of k and estimators of k are investigated. Properties of the likelihood function of k based upon the order statistics are studied. We conclude that a mixture model analysis performs…