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不完整列联表中的准独立性与最大似然估计AI 解读

Many authors have been concerned with contingency tables containing cells which are missing, a priori zero or otherwise specified. This article examines the problem of maximum likelihood estimation for such tables under the “quasi-in-dependence” model. In particular, conditions are provided to ensure the existence of unique nonzero maximum likelihood estimates for the cells of incomplete tables obtained by deleting the missing or a priori zero cells, even when other cells…

由标记有丝分裂比例曲线进行统计推断AI 解读

The fraction labelled mitoses curve is widely used to study the premitotic phase of the cell cycle in proliferating cell populations. The population is here assumed to be in a steady state of exponential growth. The theoretical curve is derived in an explicit computational form, allowing for correlations between phases. This gives the likelihood function explicitly, and classical maximum likelihood methods of fitting the theoretical curve to experimental data can work very…

分布滞后模型分析及其在消费函数估计中的应用AI 解读

SINCE KOYCK'S pioneering work, distributed lag models have come to play an important role in econometrics and much work has been done to develop methods for analyzing them-see e.g. Koyck [15], Klein [12], Solow [20], Fuller and Martin [5], Malinvaud [18], Hannan [9], Liviatan [17], Amemiya and Fuller [1], Zellner and Park [25], Thornber [21], Waud [23], Dhrymes [3], and Griliches [7]. In the present paper we present maximum likelihood and Bayesian estimation procedures for…

线性函数关系似然曲面的鞍点AI 解读

Summary In a recent paper Solari has shown that there is no maximum-likelihood solution to the problem of estimating a linear functional relationship when both variates are subject to errors that have an unspecified bivariate normal distribution. The estimators purporting to be maximum-likelihood estimators were shown by Solari to determine a saddle point. This discovery clears up some anomalies that have been noted in the past.

随机变量线性函数的参数估计AI 解读

Summary Let W be a random variable and X be a linear function of W: X = αW + β. Given a sample of independent observations distributed as X, we wish to find maximum-likelihood estimators for the parameters α and β of the linear function. If the support of W is the whole real axis, the maximum-likelihood estimators can be found by the usual methods; in other cases restricted maximization techniques must be used. Here we restrict attention to cases in which the support is the…

摘要暂缺

含误分类二项数据的双重抽样估计方案AI 解读

Two measuring devices are available to classify units into one of two mutually exclusive categories. The first device is an expensive procedure which classifies units correctly; the second device is a cheaper procedure which tends to misclassify units. To estimate p, the proportion of units which belong to one of the categories, a double sampling scheme is presented. At the first stage, a sample of N units is taken and the fallible classifications are obtained; at the second…

摘要暂缺

含时变参数的非平稳时间序列模型拟合AI 解读

Summary We use the method of weighted least squares to estimate the time-dependent parameters of non-stationary time-series models. Approximate expressions for the bias and variance of the estimates, which could be used to assess the merits of various weight functions on the basis of “mean square error” criterion, are obtained. In Section 5, it is shown that the estimates obtained by weighted least-squares method are the same as estimates obtained by weighted…

Summary The problem of obtaining consistent estimates for structural parameters in the presence of infinitely many incidental parameters was discussed first by Neyman and Scott (1948). In this paper a maximum-likelihood method based on the conditional distribution given minimal sufficient statistics for the incidental parameters is suggested. It is proved that conditional maximum-likelihood estimates in the regular case are consistent and asymptotically normally distributed…

混合样本的分析方法AI 解读

This article describes the application of the method of moments and the maximum likelihood method to identify the population of origin of each observation when it is thought that the data are a mixture of random observations from two different populations. Specifically, four cases in which both the populations belong to the binomial, the negative binomial, the Poisson or the hypergeometric family are discussed. Both methods also yield estimates of the parameters of the…

利用分组观测估计帕累托定律AI 解读

The problem of estimating the scale parameter in the Pareto distribution from grouped observations is considered. Several estimators—the maximum likelihood estimator and four variants of least squares—are evaluated. Most of these have identical BAN properties but require nonlinear computations. A linearized BAN estimator is constructed, and numerical illustrations are provided.

混合样本的分析AI 解读

This article describes the application of the method of moments and the maximum likelihood method to identify the population of origin of each observation when it is thought that the data are a mixture of random observations from two different populations. Specifically, four cases in which both the populations belong to the binomial, the negative binomial, the Poisson or the hypergeometric family are discussed. Both methods also yield estimates of the parameters of the…

复合假设的渐近最优检验AI 解读

SummarySuppose we are given sample observations from a distribution f(X|θ1, …, θk), and it is desired to test the null hypothesis θ1 = 0 against the alternative hypothesis that θ1 ≠ 0, the values of θ2, …, θk being unknown. Various asymptotically optimal procedures for doing this are considered. It is shown that the C(α) tests used by Neyman are asymptotically equivalent to the use of the likelihood ratio test and to tests using the maximum likelihood estimators. The…

二乘二列联表中四分相关与最大似然相关估计的等价性AI 解读

The method of maximum likelihood is used to derive an estimate ψ for the correlation coefficient in a 2 × 2 contingency table with an underlying bivariate normal distribution. The estimate ψ is proved to be identical to Pearson's (1900) tetrachoric estimate rt. Hence, we give an approximate expression for the standard error of rt which is much simpler than Pearson's (1913) expression.

传染病潜伏期与传染期估计的改进AI 解读

The contagious disease model proposed by Bailey (1956a, b) predicts the frequency distribution of time intervals between the appearance of subsequent cases. Using data from households of two or three susceptibles into which a disease, measles, had been introduced, Bailey used a maximum likelihood procedure to determine various disease parameters, for example, length of the latent and infectious periods. In the original calculations, a desk calculator scoring procedure was…

随机变量序列中变点位置的推断AI 解读

Inference is considered about the point in a sequence of random variables at which the probability distribution changes. In particular, we examine a normal distribution with changing mean. The asymptotic distribution of the maximum likelihood estimate is derived and also the asymptotic distribution of the likelihood ratio statistic for testing hypotheses about the change-point. These asymptotic distributions are compared with some finite sample empirical distributions.

摘要暂缺

传染病潜伏期与传染期估计的改进AI 解读

The contagious disease model proposed by Bailey (1956a, b) predicts the frequency distribution of time intervals between the appearance of subsequent cases. Using data from households of two or three susceptibles into which a disease, measles, had been introduced, Bailey used a maximum likelihood procedure to determine various disease parameters, for example, length of the latent and infectious periods. In the original calculations, a desk calculator scoring procedure was…

逆线性回归的贝叶斯视角AI 解读

The model considered in this paper is simple linear regression , and the problem is to make statistical inferences about an unknown value of x corresponding to one or more additional observed values of y. The maximum likelihood estimator x of x and the classical (1 - α) 100% confidence set S for x have some undesirable properties. For example, has infinite mean square error and > 0. The purpose of this paper is to demonstrate that insight and understanding, as well as a…

允许平局的 Bradley–Terry 配对比较模型扩展AI 解读

This study is concerned with the extension of the Bradley-Terry model for paired comparisons to situations which allow an expression of no preference. A new model is developed and its performance compared with a model proposed by Rao and Kupper. The maximum likelihood estimates of the parameters are found using an iterative procedure which, under a weak assumption, converges monotonically to the solution of the likelihood equations. It is noted that for a balanced paired…

二项变量序列中变点的统计推断AI 解读

The problem of making inferences about the point in a sequence of zero-one variables at which the binomial parameter changes is considered. The asymptotic distribution of the maximum likelihood estimate of the change-point is derived in computable form using random walk- results. The asymptotic distributions of likelihood ratio statistics for testing hypothesis about the change-point are also obtained. Some exact numerical results for these asymptotic distributions are given…

基于标记有丝分裂比例曲线的统计推断AI 解读

The fraction labelled mitoses curve is widely used to study the premitotic phase of the cell cycle in proliferating cell populations. The population is here assumed to be in a steady state of exponential growth. The theoretical curve is derived in an explicit computational form, allowing for correlations between phases. This gives the likelihood function explicitly, and classical maximum likelihood methods of fitting the theoretical curve to experimental data can work very…

利用鸟环回收估计成年鸟逐年存活率与报告率AI 解读

A probability model consisting of a product of multinomial distributions is derived for a bird banding experiment in which a new batch of banded birds is released at the beginning of each year and the bands from the dead birds are returned by observers in subsequent years. The survival and reporting probabilities are assumed to vary from year to year and maximum likelihood estimates of these probabilities together with their asymptotic variances are derived. A goodness of…