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Probit 模型估计量的小样本性质AI 解读

When maximum likelihood estimates of the coefficients in a nonlinear model such as the probit model are obtained there are a number of asymptotically equivalent covariance matrix estimators that can be used. These covariance matrix estimators are typically associated with different computer algorithms. For example, with the Newton–Raphson algorithm the inverse of the negative of the Hessian matrix from the log-likelihood function is used; with the method of scoring the…

任意底层分布下方差分量估计的比较AI 解读

Large-sample covariance matrices for the analysis of variance (ANOVA), minimum norm quadratic unbiased estimator (MINQUE), restricted maximum likelihood (REML), and maximum likelihood (ML) estimates of variance components are presented for the unbalanced one-way model when the underlying distributions are not necessarily normal. The limiting variances depend on the design sequence, on the actual values of the variance components, and on the kurtosis parameters of the…

整数参数模型的统一处理AI 解读

It is shown that there is an analog to the score function (the derivative of the log-likelihood with respect to the parameter), here called the difference score, which plays an important theoretical role in integer parameter models. A unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score (LDS). It is established that many of the exact results available for exponential family models also hold…

整数参数模型的统一处理AI 解读

It is shown that there is an analog to the score function (the derivative of the log-likelihood with respect to the parameter), here called the difference score, which plays an important theoretical role in integer parameter models. A unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score (LDS). It is established that many of the exact results available for exponential family models also hold…

多元岭回归AI 解读

A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p × q parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the ‘across regression’ correlations, and ignores the Stein effect. A remedy was offered by Brown & Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting…

Frank 二元分布族AI 解读

This paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent. The proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the Fréchet bounds as well as the distribution corresponding to independent variables. Three nonparametric estimators of the association parameter are suggested and Monte Carlo experiments are used to…

含噪信号的可变潜伏期：脑电位数据的估计与检验AI 解读

The electric response of the brain related to some event, i.e. stimulus, is usually estimated by repeated stimulation and subsequent averaging of the activity recorded time-locked to the stimulus. The present paper deals with the model that the single responses may have varying latency, i.e. arrival time, after stimulus onset. For estimating the single latencies, a maximum likelihood approach employing iterative Fisher-scoring is developed. Further a statistic for testing on…

二维格点上的内蕴自回归及相关模型AI 解读

Stationary autoregressions on a two-dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary.Prediction formulae and the asymptotic behaviour of the semivariogram are derived.For parameter estimation we propose an approximate maximum likelihood estimator, a generalization of Whittle's estimator; it is derived also for general intrinsic models.

一阶自回归参数的渐消加权估计AI 解读

In the estimation of autoregressive parameters, biases from ordinary least-squares or maximum likelihood estimator are big even for moderately large sample sizes. A new tapering estimation technique is developed to reduce the bias. Monte Carlo experiments show that the tapering estimation in the time domain yields a substantial reduction in the bias when autoregressive parameters are positive and not very near unity, over a wide range of sample sizes.

任意变量子集含相关或不相关测量误差时的回归一致估计集合AI 解读

OVER THE LAST DECADE the problem of measurement errors in the independent variables of a regression equation has attracted renewed interest among econometricians. In the fifties and sixties, the problem was considered to be more or less hopeless due to its inherent underidentification (e.g., Theil (1971)). Apart from instrumental variables, the most frequently cited textbook solution was Wald's method of grouping (Wald (1940)). Recent insight into the properties of the…

基于偏差函数的 M 估计量的一致性AI 解读

SUMMARY In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-parameter and a regression setting, we give some general conditions under which a DMBE is consistent. For a suitable weighting scheme, these conditions are satisfied in many…

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Beta–二项模型的贝叶斯估计与预测AI 解读

The beta-binomial distribution, which is generated by a simple mixture model, has been widely applied in the social, physical, and health sciences. Problems of estimation, inference, and prediction have been addressed in the past, but not in a Bayesian framework. This article develops Bayesian procedures for the beta-binomial model and, using a suitable reparameterization, establishes a conjugate-type property for a beta family of priors. The transformed parameters have…

利用递减密度极大似然估计的均匀分布单调经验贝叶斯检验AI 解读

An empirical Bayes test for testing $\vartheta \leq \vartheta_0$ against $\vartheta > \vartheta_0$ for the uniform distribution on $\lbrack 0, \vartheta)$ is discussed. The relation is shown with the estimation of a decreasing density on $\lbrack 0, \infty)$ and a monotone empirical Bayes test is derived based on the least-concave majorant of the empirical distribution function. The asymptotic distribution of the Bayes risk is obtained and some Monte Carlo results are given.

协方差矩阵的比例关系AI 解读

The present paper considers inference for the statistical model specifying proportionality between independent Wishart distributions. It is shown that the maximum likelihood estimate of the common covariance matrix and the constants of proportionality is the unique solution to the likelihood equation and an iterative procedure determining the estimator is given. The model is an exponential transformation model, which implies the existence of an exact ancillary (a maximal…

回归自适应最大似然估计的 Monte Carlo 证据AI 解读

This paper reports Monte Carlo evidence on the fixed sample size properties of adaptive maximum likelihood estimates of a linear regression. The focus is on the problem of selecting the smoothing and trimming parameters used in estimating the score function. We examine the performance of adaptive maximum likelihood estimators when these parameters are preselected or, alternatively, are determined by a data-based bootstrap method.

乘法强度模型中的筛法极大似然估计AI 解读

For point processes comprising i.i.d. copies of a multiplicative intensity process, it is shown that even though log-likelihood functions are unbounded, consistent maximum likelihood estimators of the unknown function in the stochastic intensity can be constructed using the method of sieves. Conditions are given for existence and strong and weak consistency, in the $L^1$-norm, of suitably defined maximum likelihood estimators. A theorem on local asymptotic normality of…

列联表关联模型中的顺序约束评分参数AI 解读

The row effects and column effects models for two-way contingency tables have parameters for the row and column categories pertaining to the association between the variables. For classifications having ordered categories, it is often reasonable to assume that the association parameters have a corresponding ordering. This article proposes order-restricted estimates of the association parameters in these models. The maximum likelihood solution can be determined by the…

非标准条件下最大似然估计与似然比检验的渐近性质AI 解读

Large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described. Specifically, the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived. These results generalize the work of Moran (1971), Chant (1974), and Chernoff (1954). Some of Chant's results are shown to be incorrect. The approach used in deriving these results follows from comments made by Moran…

通过数据增广计算后验分布AI 解读

The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by…

随机截断数据的影响曲线AI 解读

Under a random truncation model, observations (X, Y) are lost if X < Y. Properties of the maximum likelihood estimators for the distributions F, G of X and Y and the truncation proportion a have been treated by various authors, for example, Lynden-Bell (1971), and more recently Woodroofe (1985). Asymptotic variances of various estimates, including the mean, the median, the L- and the M-estimates and â, if they can be expressed as functionals of ^ and Ĝ, are obtained through…

因子分析及相关模型中统计推断的稳健性AI 解读

A class of latent variable models which includes the unrestricted factor analysis model is considered. It is shown that minimum discrepancy test statistics and estimators derived under normality assumptions retain their asymptotic properties when the common factors are not normally distributed but the unique factors do have a multivariate normal distribution. The minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic…

具有嵌套层级超泊松变异的广义线性模型AI 解读

We consider a scaled Poisson generalized linear model with random multiplicative errors associated with each stratum of a nested block structure. The normal equations are obtained. The quasi-likelihood is shown to be the product of a sequence of negative binomial quasi-likelihoods using weighted totals and correcting for margins. This is achieved by extending the definition of the quasi-likelihood which now includes a vector of weights. The usual asymptotic results still…

拟似然估计的效率AI 解读

A quasi-likelihood method has been proposed by Wedderburn (1974) for the estimation of parameters in regression models when there is some assumed relationship between the mean and variance of each observation but not necessarily a fully specified likelihood. If the underlying distribution comes from a natural exponential family the quasi-likelihood estimates maximize the likelihood and so have full asymptotic efficiency; under more general distributions there is some loss of…