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通过线性规划求配对比较的最大似然排序AI 解读

The problem of ranking n objects from ‘best’ to ‘worst’, using the results of a paired comparison experiment, is formulated as a linear programming problem with the logarithm of the likelihood as the objective function. The constraints are determined by the transitivity relationships implied in a ranking. The linear program will determine maximum likelihood rankings for the k fold replicated paired comparison experiment with or without the possibility of ties. The method is…

两阶段回归模型交点的统计推断AI 解读

We study the problem of estimating and making inferences about the intersection in a two-phase regression model with one independent variable. In particular we derive an asymptotic distribution for the maximum likelihood estimate of the intersection which is a good finite sample approximation. We also discuss the associated problems of testing hypotheses about the intersection.

正态混合分布成分的估计AI 解读

The problem of estimating the components of a mixture of two normal distributions, multivariate or otherwise, with common but unknown covariance matrices is examined. The maximum likelihood equations are shown to be not unduly laborious to solve and the sampling properties of the resulting estimates are investigated, mainly by simulation. Moment estimators, minimum χ2 and Bayes estimators are discussed but they appear greatly inferior to maximum likelihood except in the…

多元线性回归模型中的经验贝叶斯估计AI 解读

Empirical Bayes estimators for the parameters in the general linear regression model are presented. These estimators by-pass exact knowledge of the prior distribution of the parameters by means of supplementary information from similar independent experiments. Indexing quantities are obtainned which summarize the information containe in a typical experimental situation, an Monte Carlo simulation is employed to determine the degree of mean square improvement of empirical…

将残差用作伴随变量AI 解读

Suppose that there is correlation between the yields of successive or adjacent experimental units. An estimator of treatment effects using the residuals of adjacent plots as a concomitant variable is investigated. It is shown to be very close to the maximum likelihood estimator when the errors form a first-order autoregressive series.

单侧与双侧删失正态样本参数的迭代极大似然估计：勘误材料AI 解读

In Table 5, on page 211, the tabular value of AV(μ^) for q1 = 0.0 and q2 = 0.9 should read 0.890, not 0.089. On page 207, on line 1, changes1 to r1; on line 2, change μ to μ^ in the expression for σ^⁠; on line 4, change §5 to §4. The following paper, of which we were not aware at the time our paper was published, should be added to the list of references: ISIDA, M. & TAGAMI, S. (1959). The bias and precision in the maximum likelihood estimation of the parameters of normal…

多变量成对比较：单变量模型的扩展及估计与检验AI 解读

This study is concerned with the development of an extension of the Bradley-Terry model for paired comparisons to situations in which responses to paired comparisons are obtained on each of several characteristics. At the outset a probability model for multivariate paired comparisons is proposed that may be represented in several distinct ways. An iterative procedure for obtaining maximum-likelihood estimates of the parameters introduced into the model is given and its…

有限总体抽样理论的一种传统路径AI 解读

The main objective of this work is to relate classical inference and sampling theory (and current sampling practice) to recent advances toward formalizing and unifying the theory of sampling from finite populations. It is pointed out that the use of definitions which coincide with what seem to be the traditional notions of simple random sampling, and post-stratification (stratification after sampling) leads to the solution of such riddles which appear in the more recent…

转移概率的极大似然与贝叶斯估计AI 解读

In this paper, maximum likelihood and Bayesian methods are presented for estimating transition probabilities when data in the form of aggregated proportions are available. The probability function for the observed proportions is assumed to have a multinomial distribution under the Lexis scheme. The multivariate beta distribution is used as the prior probability density function in formulating the Bayesian estimator. The results of some Monte Carlo experiments provide some…

似不相关回归不同估计量的小样本性质AI 解读

A Monte Carlo experiment is carried out to examine the small sample properties of five alternative estimators of a set of linear regression equations with mutually correlated disturbances. The estimators considered are ordinary least squares, Zellner's two-stage Aitken, Zellner's iterative Aitken, Telser's iterative, and maximum likelihood. The experiment, based on 100 samples, provides approximate sampling distributions for samples of size 10, 20 and 100 for various model…

双端删失样本下第一类极值渐近分布参数的最大似然估计AI 解读

Let X be a random variable having the first asymptotic distribution of smallest (largest) values, with location parameter u and scale parameter b, b > 0. The natural logarithm of the likelihood function of a sample of size n from such a distribution, the lowest r1 and the highest r2 sample values having been censored, is written down and its first and second partial derivatives with respect to the parameters are worked out. The likelihood equations, obtained by equating to…

关于最小二乘估计效率的一则札记AI 解读

Summary A linear model is considered in which errors are independent and identically distributed with zero mean. If the error distribution is specified, except possibly for unknown parameters, the asymptotic efficiency of least-squares estimates relative to maximum-likelihood estimates can be found. For regression parameters orthogonal to the general mean the asymptotic efficiency, which is independent of the design matrix, is calculated explicitly for an Edgeworth series,…

存在缺失观测时多元正态分布的参数估计AI 解读

In this paper a method is developed for estimating the parameters in the multivariate normal distribution in which the missing observavations are not restricted to follow certain patterns as in most previous papers. The large sample properties of the estimators are discussed. Equivalence with maximum likelihood estimators has been established for a subclass of problems. The results of some simulation studies are provided to support the theoretical development.

利用删失样本估计对数正态分布参数AI 解读

Let g(x) be the ratio of the ordinate and the probability integral of a standardized normal distribution. The local approximation g(x) ≃α + βx is used to derive estimators μc, σc and τc of the parameters of a log-normal distribution, from a type II censored sample. The asymptotic variances and covariances of these estimators are obtained. The estimators are shown to be asymptotically as efficient as the maximum likelihood estimators. Numerical example is presented to give an…

抽样调查的一种新估计理论AI 解读

A new estimation theory for sample surveys is proposed, the basic feature of which is a special parametrization of finite populations based on the assumptions that a character attached to the units is measured on a known scale with a finite set of scale points. In the class of estimators which do not functionally depend on the identification labels preattached to the units, the following results are proved: (1) For simple or stratified simple random sampling without…

p 依赖时间序列离散程度趋势检验中 Cox–Stuart 检验的渐近相对效率AI 解读

Cox and Stuart's tests (Cox & Stuart, 1955) are applied to test for trend in dispersion of a p-dependent time series. For a particular trend model the asymptotic relative efficiencies are obtained for the S1 and S2 tests relative to the teat based on the maximum likelihood estimate.

近似设定与 k 类估计量的选择AI 解读

This paper carries on work in [2] and [4] on the asymptotic effects of small specification error in simultaneous equation estimation. The specification errors considered are inherent in the approximate nature of econometric models. It is shown that for any parameter and small enough specification error, the probability limits of two-stage least squares and limited-information maximum-likelihood, while different, lie on the same side of the true parameter value, the…

非中心卡方变量非中心参数的最大似然估计AI 解读

The maximum likelihood estimate for the non-centrality parameter of a non-central χ2 distribution with two degree of freedom is obtained. This estimate is expressed as a solution of an equation involving Bessel functions of order 0 and 1, of purely imaginary argument, both of which are tabulated. The derivation rests mainly on a lemma dealing with limit and monotonicity properties of a function representable as a quotient of two Bessel functions. An asymptotic result is also…

摘要暂缺

引入折扣权重的估计方法AI 解读

Summary In the estimation of the parameters in time series models arising in economic and business situations, it is often of value to introduce some method of discounting which produces updated estimators that give more weight to recent data than to that arising in the distant past. The simplest methods of introducing such discounting are to modify the traditional methods of estimation. Such modifications are discussed for the methods of moments, least squares and maximum…

移位泊松分布：B 参数区域AI 解读

The two-parameter (λ, r) probability function which arises from a generalization, px =λpx -1/(x+r), of the recurrence relationship between successive probabilities of a Poisson process, has been termed the ‘Displaced Poisson Distribution’ and is considered here over the parameter space λ > 0, r ≤ 0. Properties of the distribution are examined and estimators, when r is known and unknown, are derived by the methods of moment(s) and first frequency and by maximum likelihood.…

摘要暂缺

种群与群落生态学中的多元对数级数分布及其统计性质AI 解读

A growing interest has been witnessed in recent years in multivariate discrete probability models. The multivariate logarithmic series distribution (LSD) is a multivariate analogue of the univariate LSD. This paper investigates the marginal and the conditional distributions of the multivariate LSD. It records its moment properties and also provides some regression and correlation analysis. An interesting modal property of the distribution is discovered. The paper also…

矩阵导数在多元分析中的若干应用AI 解读

It is claimed that the reasons for using matrices of derivatives, in appropriate situations, are as compelling as those for using matrices. This paper provides basic material for such use. Different types of matrix derivatives are defined and illustrated. Simple and easy techniques are then derived and are shown to be applicable to a considerable collection of matrix functions. Applications are made to such problems as establishing matrix integrals from scalar ones,…