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I 型删失下 Weibull 分布参数的估计AI 解读

The authors propose estimators for the shape and the scale parameters in the Weibull distribution under Type I censoring. They derive exact moments of the estimator for the shape parameter and establish the joint asymptotic normality of both estimators. The proposed estimators, compared with the corresponding maximum likelihood estimators, provide a simpler procedure while maintaining high asymptotic relative efficiencies for a wide range of censoring levels. Estimation of…

具有正依赖的多元二元数据建模与推断AI 解读

A model is proposed for multivariate binary data that incorporates positive dependence among components in a natural way. The model is derived from reliability-theoretic concepts, but is regarded as appropriate for analysis of multivariate binary data in any field when positive dependence is an appropriate assumption. Maximum likelihood estimation by iterative solution of likelihood equations is discussed for the general model, and asymptotically efficient estimates are…

经济时间序列中缺失观测的估计AI 解读

Two related problems are considered. The first concerns the maximum likelihood estimation of the parameters in an ARIMA model when some of the observations are missing or subject to temporal aggregation. The second concerns the estimation of the missing observations. Both problems can be solved by setting up the model in state space form and applying the Kalman filter.

单样本寿命表数据的拟合优度检验AI 解读

Grouped censored data are common in life testing, medical trials, and other fields. Individuals, subject to a disease, have their lifetimes recorded as belonging to a certain interval. If the individuals are censored or removed before death, then it is only known that their lifetimes were at least as great as the beginning of the interval in which the individuals were censored. A goodness-of-fit problem is to test the agreement of a hypothesized survival curve with the…

具有正相依性的多元二元数据建模与推断AI 解读

A model is proposed for multivariate binary data that incorporates positive dependence among components in a natural way. The model is derived from reliability-theoretic concepts, but is regarded as appropriate for analysis of multivariate binary data in any field when positive dependence is an appropriate assumption. Maximum likelihood estimation by iterative solution of likelihood equations is discussed for the general model, and asymptotically efficient estimates are…

降低持续期计量模型对分布假设敏感性的方法AI 解读

Conventional analyses of single spell duration models control for unobservables using a random effect estimator with the distribution of unobservables selected by ad hoc criteria. Both theoretical and empirical examples indicate that estimates of structural parameters obtained from conventional procedures are very sensitive to the choice of mixing distribution. Conventional procedures overparameterize duration models. We develop a consistent nonparametric maximum likelihood…

摘要暂缺

用于极大似然估计及稳健替代准则的迭代重加权最小二乘AI 解读

SUMMARY The scope of application of iteratively reweighted least squares to statistical estimation problems is considerably wider than is generally appreciated. It extends beyond the exponential-family-type generalized linear models to other distributions, to non-linear parameterizations, and to dependent observations. Various criteria for estimation other than maximum likelihood, including resistant alternatives, may be used. The algorithms are generally numerically stable,…

摘要暂缺

《散布矩阵的稳健性与效率性质》更正AI 解读

The notation used in defining the likelihood ratio statistics, ln,H,9(⁠Λ^n⁠), on p. 416, line 3 from bottom, should have the argument Λ^n deleted. For finite sample sizes, the likelihood ratio statistic is not necessarily strictly a function of the maximum likelihood estimator Λ^n⁠. The results of §4 remain valid.

关于 Daniels 最大似然估计渐近有效性证明的一则札记AI 解读

A corrected proof of an important preliminary result of Daniels (1961) is presented. Daniels's work, showing that a well-behaved second dericative of the expected log likelihood function, rather than of the log likelihood function, is the key to asymptotic efficiency, is thus complete.

线性结构关系参数估计对误差方差比选择的敏感性AI 解读

Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. The use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error…

随机实验中非线性回归遗漏协变量导致的处理效应估计偏差AI 解读

Certain important nonlinear regression models lead to biased estimates of treatment effect, even in randomized experiments, if needed covariates are omitted. The asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates. The asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential, and, in regular cases, this is a…

条件似然方法的渐近效率AI 解读

SUMMARY This paper concerns the efficiency of the conditional likelihood method for inference in models which include nuisance parameters. A new concept of ancillarity, asymptotic weak ancillarity, is introduced. It is shown that the conditional maximum likelihood estimator and the conditional score test of 0, the parameter of interest, are asymptotically equivalent to their unconditional counterparts, and hence are asymptotically efficient, provided that the conditioning…

含变点的风险率模型中的估计AI 解读

This paper discusses the estimation of parameters in hazard rate models with a change-point. Due to the irregularity of the models, the classical maximum likelihood method and the method of moments cannot be used. A consistent estimator of the change-point is obtained by examining the properties of the density represented as a mixture. The performance of the estimator is checked via simulation.

高斯自回归移动平均模型大样本极大似然估计量的直接表示AI 解读

SUMMARY A simple procedure is described for obtaining the estimator of the parameters of an autoregressive-moving average process. The estimator is derived from the maximum likelihood procedure assuming Gaussian residuals by making two simplifying assumptions which are negligible in large samples. Components of the estimator are expressed as linear combinations of a suitable set of sample serial correlations or as a rational function of such linear combinations.

家族数据中类间相关系数的估计AI 解读

SUMMARY The maximum likelihood estimates of the parent-child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given. Also given are two alternative sets of estimates which are easier to compute than the maximum likelihood estimates. Using these estimates, a test for the interclass correlation to be zero requires only the ordinary Student's t-distribution. Similarly other tests use only known distributions.…

无符号方向数据的分布无关区间估计方法AI 解读

A method of moments is suggested for large samples of unsigned directional data. The point estimators obtained coincide with the natural estimates obtained from maximum likelihood estimation if the data have a Bingham distribution. However, the calculations necessary for interval and regional estimation are considerably simpler. The statistical analysis is based upon the asymptotic sampling properties of principal components in nonnormal populations (Davis, 1977; Tyler,…

空间回归中残差协方差模型的最大似然估计AI 解读

We describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters. Observations are assumed to be Gaussian. We give conditions which ensure consistency and asymptotic normality of the estimators. Our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small…

捕获—再捕获实验中泊松与多项模型的统计推断AI 解读

The classical multinomial model used for estimating the size of a closed population is compared to the highly flexible Poisson models introduced by Cormack (1981). The multinomial model, and generalizations of it which allow for dependence between samples, may be obtained from that of Cormack by conditioning on the population size. The maximum likelihood estimators for N, the population size, and θ, the vector of parameters describing the capture process, are the same in…

二元回归模型中的变量测量误差AI 解读

We consider binary regression models when some of the predictors are measured with error. For normal measurement errors, structural maximum likelihood estimates are considered. We show that if the measurement error is large, the usual estimate of the probability of the event in question can be substantially in error, especially for high risk groups. In the situation of large measurement error, we investigate a conditional maximum likelihood estimator and its properties.

Logistic回归模型中最大似然估计的存在性AI 解读

The problems of existence, uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature (Haberman, 1974, Chapter 2; Wedderburn, 1976; Silvapulle, 1981). For multinomial logistic regression models, we prove existence theorems by considering the possible patterns of data points, which fall into three mutually exclusive and exhaustive categories: complete separation, quasicomplete separation and overlap. Our…

极大似然型方程泛函解的唯一性与 Fréchet 可微性AI 解读

Solutions of simultaneous equations of the maximum likelihood type or $M$-estimators can be represented as functionals. Existence and uniqueness of a root in a local region of the parameter space are proved under conditions that are easy to check. If only one root of the equation exists, the resulting statistical functional is Frechet differentiable and robust. When several solutions exists, conditions on the loss criterion used to select the root for the statistic ensure…

捕获—再捕获模型的检验、点估计与置信集AI 解读

A capture-recapture model that depends on the “catch-ability” of the individuals in a closed population is considered. A test is derived to decide if the capture efficiencies are the same for two capture attempts. The test given assumes no a priori information about the population and can be used even if one is dealing with relatively small populations. Statistical inferences are drawn about the size of the population. In particular, a family of point estimators for the…