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具有线性结构的协方差矩阵的渐近有效估计AI 解读

One or more observations are made on a random vector, whose covariance matrix may be a linear combination of known symmetric matrices and whose mean vector may be a linear combination of known vectors; the coefficients of the linear combinations are unknown parameters to be estimated. Under the assumption of normality, equations are developed for the maximum likelihood estimates. These equations may be solved by an iterative method; in each step a set of linear equations is…

指数族中Wald大样本检验统计量的非中心收敛AI 解读

It is shown that under very mild assumptions Wald's large-sample test statistic (quadratic form based on unrestricted maximum likelihood estimators) converges to noncentral chi-square under a sequence of local alternatives of the order $n^{-\frac{1}{2}}$, when the family of distributions is assumed to be of exponential type. This eliminates, for these families, the necessity of invoking the strict regularity conditions of Wald for the purpose of justifying the asymptotic…

高斯自回归移动平均模型的最大似然辨识AI 解读

Closed form representations of the gradients and an approximation to the Hessian are given for an asymptotic approximation to the log likelihood function of a multidimensional autoregressive moving average Gaussian process. Their use for the numerical maximization of the likelihood function is discussed. It is shown that the procedure described by Hannan (1969) for the estimation of the parameters of one-dimensional autoregressive moving average processes is equivalent to a…

具有随机进入与退出的马尔可夫链推断AI 解读

Models suitable for statistical inference in Markov chains are considered featuring various forms of stochastic entry, including Poisson, renewable binomial pool, uncertain pool size, negative binomial, and input-output reservoir. A parallel inactive states model is suggested for exit. Maximum likelihood estimates are obtained and likelihood ratio tests derived. An application is made to the distribution of Ninth Federal Reserve District member banks with respect to the…

双变量指数分布参数的估计与假设检验AI 解读

Statistical properties of the bivariate exponential distribution are investigated. Maximum likelihood and method of moments type estimates are obtained and compared with the estimates given by Arnold. The method of moments type estimates are easy to compute and highly efficient, whereas the maximum likelihood estimates are computationally inconvenient. The problem of testing for correlation in the bivariate exponential distribution is also investigated.

具有随机进入与退出机制的马尔可夫链推断AI 解读

Models suitable for statistical inference in Markov chains are considered featuring various forms of stochastic entry, including Poisson, renewable binomial pool, uncertain pool size, negative binomial, and input-output reservoir. A parallel inactive states model is suggested for exit. Maximum likelihood estimates are obtained and likelihood ratio tests derived. An application is made to the distribution of Ninth Federal Reserve District member banks with respect to the…

不同估计程序下量化反应模型参数估计的一阶偏差AI 解读

To estimate the parameters in a quantal response model, various alternative procedures have been used. A comparison is made between maximum likelihood, minimum chi-squared and modified minimum chi-squared in terms of first-order bias of parameter estimates, with particular reference to the standard probit model. It is shown that, in this respect, the procedures may differ widely, with maximum likelihood seeming the most satisfactory of the three alternatives.

T HE purpose of this paper is to point out how the efficient instrumental-variables technique discussed by Brundy and Jorgenson (1971) can be modified to take into account auto-regressive properties of the error terms. The limited-information and full-information estimators proposed in this paper are consistent and have the same asymptotic distributions as the limited-information and full-information maximum likelihood estimators, respectively. The full-information…

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两个正态密度混合模型中矩估计与最大似然估计的比较AI 解读

Assuming common variance, the moment estimators of a mixture of two normal densities are obtained. The asymptotic covariance matrix of the moment estimators and the information matrix are then derived and hence the efficiency of the moment method computed.

底层分布的选择与自适应估计AI 解读

In our approach to adaptive inference, selection of the true underlying family of distributions is needed. A Bayesian selection rule, which is based on non-informative priors for the parameters, and a multiple decision solution, that maximizes the weighted sum of the probabilities of correct selection, are presented; both of these yield a decision rule of the same form. A modified maximum likelihood solution is also given and is used to construct an adaptive estimate of the…

IN THEIR ARTICLE [5], Liu and Breen propose a new estimator of the large-sample asymptotic covariance matrix for the limited information maximum likelihood estimator in simultaneous equations, and express surprise that their estimator is different from the estimator proposed by Chernoff and Divinsky [1]. Additionally, they question the interpretation of a statistic used in the past to test over-identifying restrictions.

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Ⅰ型极值分布下未来m次观测最大值的置信上限AI 解读

The Type 1 extreme value distribution is often used as a model when the maximum of a set of future observations is the unknown quantity of interest. The tables presented in this paper provide an upper confidence limit on the maximum of a set of m future observations from a Type 1 extreme value distribution. The tables are based on the maximum likelihood estimates of the parameters from past data.

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2 × s × t 列联表的交互作用检验AI 解读

SUMMARY The interaction test for 2 x 2 x t contingency tables of Zelen (1971) is extended to 2 x 8 x t tables. This test is related to the tests of partial association, or 'main effect', of Birch (1965) and Armitage (1966). These tests are frequency analogues of the log-frequency tests con- sidered by Plackett (1962) and Goodman (1964). The various analyses are illustrated and compared in several numerical examples. Bartlett (1935) considered a model and statistical analysis…

有限遍历马尔可夫链转移概率估计中的初始状态选择AI 解读

The properties of the maximum likelihood estimators for the transition probabilities in a two-state ergodic Markov chain depend upon the choice of the initial states. For example, the initial states may be suitably fixed in advance or may be observed from the equilibrium distribution of the chain. A large number of relatively short realizations are assumed available and the asymptotic variances are examined in some detail. The relevant asymptotic covariance matrices are…

非线性函数关系的广义最小二乘与最大似然估计AI 解读

Summary A non-linear functional relationship between two mathematical variables is postulated. Departures of observed random variates from the mathematical variable values are assumed to have zero mean and general but known covariance matrix. Assuming normality we obtain by maximum likelihood an expression for the asymptotic covariance matrix of the structural parameter estimates. The expression involves a certain matrix Ψ. A generalized least squares method is proposed…

对数线性模型分析AI 解读

Summary Log-linear models are extensively used to analyse categorical and “stimulus-response” data. This paper gives an iterative procedure for obtaining maximum likelihood estimates of cell frequencies and of the parameters of a log-linear model in a multinomial experiment.

计量经济学：统计基础与应用AI 解读

1. Elementary Aspects of Multivariate Analysis.- 1.1 Preliminaries.- 1.2 Joint, Marginal, and Conditional Distributions.- 1.3 A Mathematical Digression.- 1.4 The Multivariate Normal Distribution.- 1.5 Correlation Coefficients and Related Topics.- 1.6 Estimators of the Mean Vector and Covariance Matrix and their Distribution.- 1.7 Tests of Significance.- 2. Applications of Multivariate Analysis.- 2.1 Canonical Correlations and Canonical Variables.- 2.2 Principal Components.-…

季度回归方程中四阶自相关的检验AI 解读

A test for fourth order autocorrelation in the error term of a regression equation estimated from quarterly data is described. The development draws on the finite sample results of Durbin and Watson and illustrates how their procedure for the first order case can be generalized. In the model y = X,B + u where X is a matrix of fixed regressors and u, = put-4 + Bt, an appropriate test statistic for Ho: p = 0 is the statistic d4 = {z- )2/z2 computed from the least squares…

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线性回归中二次曲线异常值的模型AI 解读

A model to describe a linear regression where outliers follow a quadratic regression is introduced and the asymptotic and small sample properties of the maximum likelihood estimators studied. The investigation demonstrates that parameter estimation in models which describe outlier patterns can provide a useful analytic procedure.

截断参数分布中 MVU 与 ML 分布函数估计量的比较AI 解读

The ratio of integrated mean square errors for minimum variance unbiased and maximum likelihood estimating distribution functions is computed for truncation parameter distributions as a relative efficiency measure. A “closeness” relative efficiency is also computed for these estimators for the same class of distributions. The MVU estimator is found to be more efficient than the ML estimator for all sample sizes exceeding two in both cases.