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单一潜变量的多指标多原因模型估计AI 解读

We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to…

任一周日：用最大似然方法公平排序竞技队伍AI 解读

This article addresses the analytic problem of obtaining fair and accurate comparisons among competitors when many pairs of them have never met and where the average quality of opposition faced may vary widely. The context studied is the National Football League's regular season of 1973. A maximum likelihood methodology is developed which simultaneously: (1) ranks all teams and (2) estimates the probabilities of upsets of various sizes. The methodology is compared with…

偏似然AI 解读

A definition is given of partial likelihood generalizing the ideas of conditional and marginal likelihood. Applications include life tables and inference in stochastic processes. It is shown that the usual large-sample properties of maximum likelihood estimates and tests apply when partial likelihood is used.

成对比较排序的极大似然估计：一种广义方法AI 解读

In many situations one is faced with the task of constructing a linear order, or ranking, of n objects based on data derived from a paired comparison experiment. Alternatively, one may desire to estimate the preference relation on the set of objects. Numerous criteria appear in the literature, and in practice, under which rankings or preferences may be selected. The main emphasis of this paper is on developing a general approach to maximum likelihood estimation of rankings…

线性与若干非线性计量模型全信息估计量的工具变量方法AI 解读

FIML is shown to be an instrumental variables estimator where the instruments embody all the over-identifying a priori restrictions. FIML is compared to the two alternative estimators 3SLS and full information instrumental variables. 3SLS differs from FIML in not using all a priori restrictions in forming the instruments. The full information instrumental variables estimator when iterated to convergence yields the FIML estimate. For the case of nonlinearity in the parameters…

统计推断中的稳定分布（二）：稳定分布样本的信息AI 解读

Large-sample theory for the estimation of parameters for a stable distribution is developed using the theory of Fisher's information. The asymptotic standard deviations and correlations of the maximum-likelihood estimates of the index, skewness, scale and location parameters are computed and tabled and used to compute the relative asymptotic efficiency of other proposed estimators. It is shown that if the true distribution is symmetric stable, the MLE's of index and scale…

以最小误分类概率为目标的线性特征选择AI 解读

We describe an approach to linear feature selection for $n$-dimensional normally distributed observation vectors which belong to one of $m$ populations. More specifically, we consider the problem of finding a rank $k k \times n$ matrix $B$ which minimizes the probability of misclassification with respect to the $k$-dimensional transformed density functions when a Bayes optimal (maximum likelihood) classification scheme is used. Theoretical results are presented which, for…

相关系数估计之间的相关性AI 解读

Expressions are derived for the asymptotic correlations between the five possible pairs of correlations, whether intraclass or interclass, when estimated by maximum likelihood from multinormally distributed samples. The use of these expressions is discussed for testing hypotheses about, and for obtaining pooled estimates of, the intraclass and interclass correlations.

有限参数随机过程族中最大似然估计一致性的一个注记AI 解读

We consider families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes it is shown that maximum likelihood estimates convergence almost surely to the correct parameter value. This established by use of a submartingale property of the sequence of maximized likelihood ratios together with a technique first employed by Wald [24] in the case of independently identically distributed random variables.

生灭过程中的最大似然估计AI 解读

Maximum likelihood estimation of the parameters $\lambda$ and $\mu$ of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The result problem of estimation from the discrete skeleton of the process is also discussed.

位置参数的自适应最大似然估计AI 解读

Consider estimators $\hat{\theta}_n$ of the location parameter $\theta$ based on a sample of size $n$ from $\theta + X$, where the random variable $X$ has an unknown distribution $F$ which is symmetric about the origin but otherwise arbitrary. Let $\mathscr{F}$ denote the Fisher information on $\theta$ contained in $\theta + X$. We show that there is a nonrandomized translation and scale invariant adaptive maximum likelihood estimator $\hat{\theta}_n$ of $\theta$ which doe…

若干非标准情形下似然比的渐近分布AI 解读

In an earlier article [8] conditions were given under which maximum likelihood estimators are asymptotically normal and asymptotically efficient in certain nonstandard cases. Under these same conditions, the asymptotic distribution of the likelihood ratio is found. An easily computed asymptotic equivalent of the likelihood ratio is developed, and is applied to a problem of testing fit.

若干非标准情形下似然比的渐近分布AI 解读

In an earlier article [8] conditions were given under which maximum likelihood estimators are asymptotically normal and asymptotically efficient in certain nonstandard cases. Under these same conditions, the asymptotic distribution of the likelihood ratio is found. An easily computed asymptotic equivalent of the likelihood ratio is developed, and is applied to a problem of testing fit.

整数受限参数空间中若干极大似然估计量的容许性与极小极大性AI 解读

Summary The present note studies the admissibility and minimaxity of maximum likelihood estimators in certain examples where the parameter space is restricted to integers.

不变正态模型AI 解读

Many hypotheses in the multidimensional normal distribution are given or can be given by symmetries or, in other words, invariance. This means that the variances are invariant under a given subgroup of the general linear group in the vector space of observations. In this paper we define a class of hypotheses, the Invariant Normal Models, including all symmetry hypotheses. We derive the maximum likelihood estimator of the mean and variance and its distribution under the…

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…

允许存活率与捕获概率不同的 K 次抽样标记重捕模型AI 解读

A K-sample tag-recapture model for an open population is derived which allows for animals with different histories of capture to have both different probabilities of survival and of future capture. Previous stochastic models are special cases of this one. Maximum likelihood estimators of the population sizes at each sampling time are derived for models allowing differing degrees of unequal survival and catchability. Methods of testing between these models are derived by…

高斯格点过程空间交互的估计与检验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.

关于几何级数物种频率模型的札记AI 解读

We consider a certain randomized geometric series of relative abundances and the limit, of the Dirichlet distribution used in the derivation of the logarithmic series distribution. When an individual is chosen at random from either of the populations, the abundance of the species it represents is shown to have the same distribution. The maximum likelihood estimate for the geometric series model with fixed abundances is evaluated, and a bias correction is proposed.

最大似然成对比较排序与二次指派AI 解读

A connexion is identified between maximum likelihood paired-comparison ranking and the problem of quadratic assignment discussed in the operational research literature. This relationship immediately gives a set of computational techniques for obtaining the necessary rankings, and, in addition, provides a general framework for testing the reasonableness of particular object sequencings suggested a priori.

分枝过程参数估计效率的几点讨论AI 解读

This paper is concerned with efficiency in the estimation of the mean θ of the offspring distribution of a supercritical Galton-Watson branching process on the basis of a sample of n consecutive generation sizes. First, a direct comparison is made between the maximum likelihood estimator and the simple ratio of generation sizes estimator. Next, a new definition of asymptotic efficiency of an estimator is given, generalizing that of Rao (1973). It is shown that, for offspring…

相关系数估计量之间的相关性AI 解读

Expressions are derived for the asymptotic correlations between the five possible pairs of correlations, whether intraclass or interclass, when estimated by maximum likelihood from multinormally distributed samples. The use of these expressions is discussed for testing hypotheses about, and for obtaining pooled estimates of, the intraclass and interclass correlations.

双变量 Probit 分析：最小卡方方法AI 解读

In this article we propose two minimum chi-square estimators for a bivariate probit model. We call one estimator the Full Information and the other Limited Information Minimum Chi-Square because the first takes account of all the a priori information while the second does not. Both estimators are shown to be consistent. Moreover, the first is shown to be asymptotically as efficient as the maximum likelihood estimator and yet is computationally much simpler. For illustration,…