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摘要暂缺

多元经验贝叶斯与协方差矩阵估计AI 解读

The problem of estimating several normal mean vectors in an empirical Bayes situation is considered. In this case, it reduces to the problem of estimating the inverse of a covariance matrix in the standard multivariate normal situation using a particular loss function. Estimators which dominate any constant multiple of the inverse sample covariance matrix are presented. These estimators work by shrinking the sample eigenvalues toward a central value, in much the same way as…

不完整多元数据的均值推断AI 解读

A class of statistics g(v) is proposed for constructing tests and confidence intervals for a linear combination of means v using an incomplete multivariate normal sample. The class includes statistics based on maximum likelihood estimates for all the data, and simpler statistics such as those based on a subset of complete observations. A simple measure of relative efficiency is proposed to decide when a simpler statistic is appropriate. For the case of two variables with…

分枝过程的有效检验AI 解读

This paper is concerned with efficiency in testing for the mean of the offspring distribution of a supercritical Galton-Watson process. It is suggested that the maximum likelihood estimator is generally inefficient for this problem in the sense that asymptotically it is not an optimum discriminator between alternative values of the parameter. Three competing tests are discussed and their efficiency compared via an example.

线性学习模型中的最大似然估计AI 解读

An extension of the Markov model with only a few additional parameters is the linear learning model, as introduced by Bush & Mosteller (1955). To help its application in biological research an iterative procedure for calculating the maximum likelihood estimates of the unknown parameters is presented. Numerical examples, some of which have already been treated by Bush & Mosteller, are included, as well as comparisons between the linear learning model and the Markov model.

双响应均有缺失时配对均值的比较AI 解读

Five procedures for testing the equality of two correlated means with incomplete data on both responses are compared by using Monte Carlo studies; three procedures were suggested by Lin & Stivers (1974) and two are suggested in this paper. The results are that the two tests based on a modified maximum likelihood estimator are to be preferred, the one due to Lin & Stivers when the number of complete pairs is large and the one proposed in this paper otherwise, provided the…

多组数据的线性结构关系AI 解读

When observations on two variables are sampled from two or more distinct populations, the linear structural relation between the two variables can be estimated consistently. The maximum likelihood estimators of the parameters in the model are found; they have different forms in different parts of the sample space. A procedure for testing hypotheses about the parameter usually of principal interest, the slope of the relation, is derived; it is complicated by the unusual…

完整列联表的改进似然比检验AI 解读

SUMMARY Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the -2 log A test statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic x2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood…

若干广义线性模型最大似然估计的存在性与唯一性AI 解读

Generalized linear models were defined by Nelder & Wedderburn (1972) and include a large class of useful statistical models. It is shown that for some of these models maximum likelihood estimates always exist and that for some others they exist provided certain degeneracies in the data do not occur. Similar results are obtained for uniqueness of maximum likelihood estimates and for their being confined to the interior of the parameter space. For instance, with the familiar…

超结构关系：函数关系与结构关系的综合AI 解读

A maximum likelihood solution is presented for a model which is a synthesis of the linear functional and structural relations. In the replicated case, the slope estimate is a root of a quadratic equation, the coefficients of which are symmetrical with respect to the within and between-groups sample covariances. In the unreplicated case it is shown that two variance ratios must be known, whereupon the slope estimator is a root of a quintic equation. When one of these variance…

状态合并观测下马尔可夫链的统计推断AI 解读

In an ( n +1)-state homogeneous Markov chain, when due to some experimental limitations n states are not observable, the maximum likelihood estimation of an unknown parameter θ is considered and the efficiency of θ relative to the most efficient estimator when all the states are observable is discussed. The study is extended to the case when there are two lumps of unobservable states in a four-state Markov chain.

Pitman 位置估计量的小样本方差AI 解读

For three symmetric distributions and six sample sizes, this article presents estimates of the small-sample variance of Pitman's location-invariant and location-scale-invariant estimators of location. It then compares these two estimators and investigates the closeness of the Cramér-Rao bound when estimators are required to be invariant. Expressions of the form c/(n − d) prove quite effective in fitting variances of Pitman estimators, and d can be interpreted as the amount…

偏差对配对匹配及分层样本相对风险估计量的影响AI 解读

Monte Carlo methods are employed to compare the effectiveness of pair-matched and independent stratified samples for estimating relative risk in the presence of bias. Three approximations to the maximum likelihood estimator for stratified samples suggested by Woolf, Mantel and Haenszel and Birch, respectively [25, 17, 2], are also compared. The sampling model is modified to approximate the practical choices for a researcher and to allow for the loss of unmatchable sample…

指数失效模型下的总体规模估计AI 解读

We are given J observations obtained by truncated sampling of a population of N items which fail independently according to the exponential distribution, where both N and the scale parameter of the exponential are unknown. Estimates of N are developed, and compared. These are conditional and unconditional maximum likelihood estimates, and a class of Bayes modal estimates. On the basis of second-order asymptotic properties, one of the Bayes estimates is singled out as most…

向量参数似然方程根唯一性的一个注记AI 解读

Two examples are given from the literature in which results concerning functions of a single variable are applied incorrectly to multivariate functions. One of the examples concerns the proof of a basic theorem in the theory of maximum likelihood estimation of vector-valued parameters. An alternate statement and proof of the theorem are given.

Logistic 回归与正态判别分析的效率比较AI 解读

A random vector x arises from one of two multivariate normal distributions differing in mean but not covariance. A training set x 1, x 2, ··· x n of previous cases, along with their correct assignments, is known. These can be used to estimate Fisher's discriminant by maximum likelihood and then to assign x on the basis of the estimated discriminant, a method known as the normal discrimination procedure. Logistic regression does the same thing but with the estimation of…

Pitman 位置估计量的小样本方差AI 解读

For three symmetric distributions and six sample sizes, this article presents estimates of the small-sample variance of Pitman's location-invariant and location-scale-invariant estimators of location. It then compares these two estimators and investigates the closeness of the Cramér-Rao bound when estimators are required to be invariant. Expressions of the form c/(n − d) prove quite effective in fitting variances of Pitman estimators, and d can be interpreted as the amount…

柯西分布似然的单峰性AI 解读

Although the likelihood for the median of a Cauchy distribution with known scale is often multimodal, the joint likelihood for both location and scale parameters has exactly one point of maximum and at most one stationary point. The maximized likelihood function is therefore unimodal. It is also suggested that the likelihood for the location, when evaluated at the maximum likelihood estimate of the scale, is unimodal considerably more often than might have been anticipated…

高斯格点过程空间相互作用的估计与检验AI 解读

Maximum likelihood estimation for rectangular lattice autonormal schemes is discussed. Explicit results for the first-order isotropic scheme are given and compared with those obtained using a simple coding technique. The efficiency of the coding technique in testing for randomness on various types of lattice is assessed.

摘要暂缺

惩罚函数法下概率密度的非参数最大似然估计AI 解读

Tne maximum likelihood estimate of a probability density function based on a random sample does not exist in the nonparametric case. For this reason and others based on heuristic Bayesian considerations Good and Gaskins suggested adding a penalty term to the likelihood. They proposed two penalty terms; however they did not establish existence or uniqueness of their maximum penalized likelihood estimates. Good and Gaskins also suggested an alternate approach for calculating…

移动平均残差自回归过程及线性结构协方差矩阵的最大似然估计AI 解读

The autoregressive process with moving average residuals is a stationary process $\{y_t\}$ satisfying $\sum^p_{s = 0} \beta_sy_{t - s} = \sum^q_{j = 0} \alpha_j\nu_{t - j}$, where the sequence $\{\nu_t\}$ consists of independently identically distributed (unobservable) random variables. The distribution of $y_1,\cdots, y_T$ can be approximated by the distribution of the $T$-component vector $\mathbf{y}$ satisfying $\sum^p_{s = 0} \beta_s\mathbf{K}_s\mathbf{y} = \sum^q_{j = 0} \alpha_j\mathbf{J}_j\mathbf{v}$…

多元分析中的缺失值AI 解读

Summary This paper presents computational results for some alternative methods of analysing multivariate data with missing values. We recommend an algorithm due to Orchard and Woodbury (1972), which gives an estimator that is maximum likelihood when the data come from a multivariate normal population. We include a derivation of the estimator that does not assume a multivariate normal population, as an iterated form of Buck's (1960) method. We derive an approximate method of…

分枝过程的方差估计AI 解读

Assume given the $(n + 1)$-first generation sizes of a supercritical branching process. An estimator is proposed for the variance $\sigma^2$ of this process when the mean is known. It is shown to be unbiased, consistent and asymptotically normal. From that one deduces a consistent and asymptotically normal estimator for $\sigma^2$ in the case of an unknown mean. Finally, the maximum likelihood estimator of $\sigma^2$, based on a richer sample, is found and asymptotic…