日期精度：到日 1310 篇 · 到月 1919 篇 · 到年 331 篇 · 未提供 1 篇
基于极大似然估计的柯西分布推断
Tables, based on maximum likelihood estimators, are presented which enable one to obtain confidence intervals and test hypotheses about parameters of the Cauchy distribution. The difficulty in obtaining the maximum likelihood estimates of the parameters is discussed. Comparisons between the maximum likelihood estimators and the best linear unbiased estimators are presented.
Logistic 分布参数的置信区间
Confidence intervals for the parameters of the logistic distribution based on maximum likelihood estimators are presented. It is shown that the maximum likelihood equations have a unique solution. Unbiasing factors for the maximum likelihood estimators of the scale parameter are given.
协方差结构分析的一般方法
It is assumed that observations on a set of variables have a multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix. Any parameter of the model may be fixed, free or constrained to be equal to other parameters. The free and constrained parameters are estimated by maximum likelihood. A wide range of models is obtained from the general model by imposing various specifications on the parametric structure of the…
方差分量估计量的均方误差效率
Various estimators of components of variance for the balanced one way layout are compared using mean squared error as a measure of performance. Several modifications of the maximum likelihood estimator and several formal Bayes estimators are compared and mean square error relationships are given. Inadmissibility is established for a large class of translation and scale invariant estimators. Numerical results are tabled and graphed to exhibit the relative efficiency of the…
用线性规划求解成对比较的最大似然排序
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…
混合移动平均与自回归系统的估计
Estimates are constructed of the parameters in mixed moving average autoregressive models based upon Fourier transformation of the data. These are shown to be asymptotically normal with the same distribution as the maximum likelihood estimators for the Gaussian case. The method extends to the vector case but the procedure is discussed in detail only for vector moving averages.
正态混合分布的成分估计
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…
T HE geometric distributed lag model developed by Koyck [8] and Nerlove [11] has been widely used in many empirical studies. The appropriate estimation method for parameters of these models is determined by the true probability distribution of random errors. If the random errors follow a first-order Markov process, Klein [7] has shown that the method of weighted regressions yields maximum likelihood estimators.' However, Klein's method requires prior knowledge of the true…
In this paper we estimate a complete system of demand equations making full use of the restrictions implied by economic theory. Our theoretical model is based on the Klein-Rubin linear expenditure system which was first estimated by Stone. We place primary emphasis on maximum likelihood estimates obtained using annual time series observations of prices and per capita consumption for the U.S. economy in the period 1948-1965. The plan of the paper is as follows: Section 1…
关于序贯估计的一则札记
Summary Moran (1951) infers that for some stationary stochastic processes, problems of parameter estimation may be simplified by employing sequential estimation procedures. He considers for example, estimation of the birth rate in the (stationary) Furry–Yule process. The purpose of this note is to indicate that Moran's suggestion may be useful for non-stationary processes as well. In particular, we consider maximum likelihood estimation of the parameter of a non-homogeneous,…
三维列联表中的卡方分解与偏关联检测
Summary This paper presents a method of partitioning a χ2 statistic for the I × J × K contingency table (viz. the χ2 statistic that is based upon the likelihood-ratio criterion for testing the null hypothesis that the three variables pertaining to the three-way table are mutually independent) into additive components that can be used to test (1) the null hypothesis of zero three-factor interaction, (2) the null hypothesis that the partial association between two of the…
非正则估计（一）：位置参数估计量的方差界
Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical lower bounds on the variance of unbiased estimators, such as the Cramér-Rao bound, lead to the trivial result V(t) ≧0, where t is…
多元线性回归模型中的经验贝叶斯估计量
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…
估计线性函数关系问题的“最大似然解”
Summary The problem considered is that of estimating a functional relationship (assumed linear) between two unobservable mathematical quantities ξ and η from pairs of observations on these quantities when both sets of observations are subject to normal independent errors. The problem has attracted much interest over a long period and one reads repeatedly that the method of maximum likelihood yields unsatisfactory estimators in this case. In this note we show that in fact no…
似然函数实例及其与点估计和大样本近似的比较
The exact likelihood functions are examined for several examples of data chosen from the literature. These are compared with the likelihoods arising from the large sample approximations and with point estimates that were actually used in the literature. It is concluded that large sample approximations (application of standard maximum likelihood theory) can be misleading for inferences and should be checked against the actual likelihood functions. Similarly point estimates…
似然实例及其与点估计和大样本近似的比较
The exact likelihood functions are examined for several examples of data chosen from the literature. These are compared with the likelihoods arising from the large sample approximations and with point estimates that were actually used in the literature. It is concluded that large sample approximations (application of standard maximum likelihood theory) can be misleading for inferences and should be checked against the actual likelihood functions. Similarly point estimates…
In their paper on the three stage least squares method of estimation of a simultaneous equation system, Zellner and Theil [5] make the interesting observation that the large sample efficiency of the estimates of the parameters in the group of over-identified equations is unaffected if the three stage method is applied to this subsystem alone, ignoring all the exactly identified equations. It is shown in this paper that the estimates themselvesnot just their large sample…
多元统计中的缺失观测（三）：简单线性回归的大样本分析
We derive the asymptotic distribution of several estimators for the parameters of the linear regression of y on x when some observations on y and on x are missing. Then, we compare estimators using a mean square error criterion. We find for example that a simple estimator of the linear regression function has asymptotic efficiency no worse than 0.95 compared with the maximum likelihood estimator (assuming bivariate normality) provided that no more than 30 per cent of the y's…
多元成对比较：单变量模型的推广及估计与检验
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…
将残差用作伴随协变量
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.
后验分布的渐近行为
Summary Let a random sample of size n be taken from a distribution having a density depending on a real parameter θ, and let θ have an absolutely continuous prior distribution with density π(θ). We give a rigorous proof that, under suitable regularity conditions, the posterior distribution of θ will, when n tends to infinity, be asymptotically normal with mean equal to the maximum-likelihood estimator and variance equal to the reciprocal of the second derivative of the…
In this paper a family of functional iterations is introduced. One member of this family is the Newton-Raphson method and another member, obtained from a generalization of Steffensen's method to a system of equations, has been considered in [7]. The general member of the family is derived from a regulafalsi construction, due to Gauss, for a particular choice of points in the iteration. From the computational point of view, all the members of the family of iterations, except…
混合移动平均自回归系统的估计
Estimates are constructed of the parameters in mixed moving average autoregressive models based upon Fourier transformation of the data. These are shown to be asymptotically normal with the same distribution as the maximum likelihood estimators for the Gaussian case. The method extends to the vector case but the procedure is discussed in detail only for vector moving averages.