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组间相关系数的最大似然估计AI 解读

The method of maximum likelihood is used to estimate a mother-child correlation, ρMS, when there are a variable number of offspring per family. The technique is iterative and uses standard Newton-Raphson procedures to facilitate convergence. A comparison is made using Monte Carlo methods between the maximum likelihood estimator and other more traditional estimators of interclass correlations. It is shown that the maximum likelihood estimator is roughly equivalent in mean…

方向数据的指数模型AI 解读

A rotationally invariant exponential model, which includes the Fisher-von Mises and Bingham distributions as special cases, is proposed for directional data in $R^p(p \geqslant 2)$. A new regression estimator for the model parameters is developed as a competitor to the maximum likelihood estimator. Both the new estimator and the MLE are asymptotically efficient at the postulated model and are robust under small departures from that model. Computationally, the regression…

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含缺失值多元回归的极大似然推断：模拟研究AI 解读

Summary Maximum likelihood inference for the coefficients of a multiple regression with missing values is studied by simulation, using artificially generated multivariate normal observations with randomly deleted missing values. The method is compared with least squares on the complete observations by mean squared error. Two methods of estimating the covariance matrix of the m.l. estimates are compared, and the applicability of large sample theory to obtain tests and…

若干多元回归问题中的一族极小极大估计量AI 解读

A family of estimators which dominate the maximum likelihood estimators of regression coefficients is given when the dependent variable and (3 or more) independent variables have a joint normal distribution.

某些序贯估计量的渐近最优性AI 解读

We give a decision-theoretic justification of a heuristic principle suggested by Robbins. Suppose a sequence $X_1, X_2, \cdots$ of independent random variables can be observed; they are known to be identically distributed with unknown mean and variance $u, \sigma^2(u)$ respectively. We assume further that the common distribution is of exponential type, so that the sample mean $\bar{X}$ is a sufficient statistic. The problem is to estimate $u$ taking into account the cost of…

基于条件设定的最大似然估计量的渐近性质AI 解读

Along with the asymptotic distribution, expressions for the asymptotic bias and asymptotic dispersion matrix of the preliminary test maximum likelihood estimator for a general multi-sample parametric model (when the null hypothesis relating to the restraints on the parameters may not hold) are derived and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators. This study reveals the robustness property of the preliminary test…

加速寿命试验的非参数方法AI 解读

A nonparametric model of acceleration is introduced. Based on this model, a procedure is suggested for estimating the nonaccelerated life distribution from accelerated observations. Unlike previous nonparametric estimation procedures, our method does not require nonaccelerated observations. A relationship between the accelerated and the nonaccelerated distributions is assumed but there is variety in that choice. A comparison of our method with the power rule method under the…

平稳多元自回归移动平均模型的似然函数AI 解读

Procedures to estimate parameters in multivariate autoregressive moving average (ARMA) models are developed. Gaussian errors are assumed. Exact maximum likelihood estimation procedures are developed for pure moving average models. Approximate procedures are obtained to estimate stationary mixed ARMA models. Properties of the estimates and an example are given.

基于诱导次序统计量的删失二元正态分布推断AI 解读

For a censored sample from a bivariate normal distribution consisting of the firstk ofn order statistics of one variable and the induced order statistics of the other variable, the maximum likelihood estimators of the parameters and the associated large sample co-variance matrix are derived. The likelihood ratio test for independence is also given and its power properties studied. These methods are useful in selection problems or in life testing situations in which…

Edgeworth 与鞍点近似及其统计应用AI 解读

Summary A simple exposition is given of Edgeworth and saddle-point approximations for some univariate, multivariate and conditional distributions. The application of these approximations to some problems of conditional statistical inference within the exponential family is illustrated. Examples connected with the time-dependent Poisson process, the von Mises distribution and with bioassay are among those studied in a little detail. Some general results are derived about…

多元正态结构化均值与协方差检验中似然比统计量的非零假设渐近分布AI 解读

The multivariate normal patterned mean and covariance matrix testing problem is studied for general one and $k$-population hypotheses. T. W. Anderson's iterative algorithm for finding the maximum likelihood estimates, the forms of the likelihood ratio tests, and asymptotic chi-square distributions of these tests under the null hypothesis are given. The nonnull asymptotic normal distribution is derived using the standard delta method. This derivation involves using several…

泊松与正态均值的星形序列估计AI 解读

A vector $\mu = (\mu_1, \cdots, \mu_n)$ is said to be upper [lower] starshaped if $\mu_{m + 1} \geqslant 0 \lbrack \leqslant \mu_{m + 1} \leqslant \bar{\mu}_m\rbrack m = 1, \cdots, n - 1$, where $\bar{\mu}_m$ is a weighted average of $\mu_1, \cdots, \mu_m$. Obtained is the maximum likelihood estimate of $\mu$ when the $\mu_i$'s are the means of $n$ Poisson or normal populations and $\mu$ is known to be starshaped. The method is applied to obtain estimators of IHRA…

含受限（删失）因变量的二元选择模型：识别与估计AI 解读

A class of statistical models which generate simultaneous equation models with both discrete and continuous endogenous variables is introduced. This class of models can also be regarded as a new class of switching simultaneous equation models which are of general interest. Identification and estimation problems are investigated. Several simple consistent two stage methods are proposed. The consistency of those estimators is proved. Two step maximum likelihood procedures are…

(NOTE: Each chapter concludes with Problems and Complements, Notes, and References.) 1. Statistical Models, Goals, and Performance Criteria. Data, Models, Parameters, and Statistics. Bayesian Models. The Decision Theoretic Framework. Prediction. Sufficiency. Exponential Families. 2. Methods of Estimation. Basic Heuristics of Estimation. Minimum Contrast Estimates and Estimating Equations. Maximum Likelihood in Multiparameter Exponential Families. Algorithmic Issues. 3.…

存在误分类和双重抽样的分类数据对数线性模型AI 解读

Errors in the collection of categorical data lead to misclassification of observed counts. Several authors have proposed a double sampling scheme. This article develops a method for analysis of double sampling data. First, a log-linear model is selected for the misclassification matrix that relates the fallible to the correct data; then another log-linear model is built on the distribution of the correct classifications. Thus, the error structure can be utilized in inference…

矩阵 von Mises–Fisher 与 Bingham 分布的极大似然估计AI 解读

It has been conjectured by Khatri and Mardia that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique. We prove that, except for small sample sizes, this conjecture is true, both in the case where the parameter matrix has known rank and in the unrestricted case. The corresponding result for the matrix Bingham distribution is proven also.

线性过程估计的高阶效率AI 解读

Estimation as a reduction of data is usually accompanied by some loss of information. This paper theoretically compares asymptotically efficient estimation methods for parameters in Gaussian linear processes. By means of the concept of "asymptotic information loss" suitably defined, estimates equivalent to the order of $N^{-\frac{1}{2}}$ are differentiated. This problem was studied by C. R. Rao for multinomial distributions and by K. Takeuchi for the exponential family of…

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ARMA 过程最大似然估计量的强一致性AI 解读

The strong consistency of the maximum likelihood parameter estimation method is established for multivariate Gaussian stochastic processes possessing autoregressive moving average (ARMA) representations. The demonstration in this paper exploits the ergodic theorem together with results from linear prediction theory.

多项分布概率的估计AI 解读

This paper deals with the estimation of the parameters (cell probabilities) of a multinomial distribution. For the binomial distribution it is known that the maximum likelihood estimator (MLE) is admissible with respect to the squared error loss. It is shown that the MLE is admissible also in the case of the multinomial distribution.

对 Schlesselman 所提变换准则的评论AI 解读

In the two-way analysis of variance with replicates, Schlesselman (1973) proposed a criterion of transformation based on classical statistics for testing homoscedasticity and additivity. He compared his criterion (Z(γ)) for selecting a transformation with the maximum likelihood estimate of Box and Cox (1964), and found Z(γ) superior in selecting a “correct” transformation when tested on models with normal and Cauchy error terms. We report here corrections of some of the…

参数函数与计量模型结构系数的最小期望损失估计AI 解读

Abstract Further sampling properties of previously derived (Zellner 1975) MELO estimates for reciprocals and ratios of parameters and for structural coefficients of econometric models are presented. Approximate small-sample moments and risk functions of MELO estimators for these problems are derived and compared with those of other well-known estimators. The exact finite sample distribution of the MELO reciprocal mean estimator is derived and compared with that of the…