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零值与部分一值缺失时截断泊松分布的估计AI 解读

This paper is concerned with maximum likelihood estimation of the Poisson parameter λ when the zero class has been truncated and when errors of observation have resulted in eliminating some though not necessarily all of the one class. Estimators are derived both for λ and the proportion θ of ones eliminated as a consequence of faulty observation. A table and a graph of the estimation function involved are given. Asymptotic variances and covariances of the estimators are…

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修正泊松分布的参数估计AI 解读

Errors in observing and reporting sample data often complicate the problem of estimating parameters of the distribution being sampled. If neglected, such errors may lead to seriously biased estimates. There exits a large general class of such estimation problems involving numerous different distributions, different types and varying degrees of observational errors. This paper is limited, however, to maximum likelihood estimation in a Poisson distribution which has been…

最大似然估计程序及其配套显著性检验AI 解读

Summary The essence of many statistical problems, including most standard techniques, is to test whether or not the unknown parameters of an appropriate statistical model satisfy certain restrictions; and the outcome of such a test dictates whether it is necessary to provide estimates of these parameters which also satisfy the restrictions. In this paper we discuss and illustrate the relative merits, as practical tools for the consulting statistician, of two large-sample…

具有充分统计量的分布样本之似然曲面曲率公式AI 解读

In this paper is given a formula for the curvature of the ‘likelihood surface’ (see §3) of a sample drawn from a distribution admitting sufficient statistics for the parameters, at the point represented by the maximum likelihood estimates (m.I.e.) of the parameters. More precisely it is shown in the case of two parameters that the negative of the trace and the determinant of Fisher's information matrix, respectively, measure the first and second (Gaussian) curvatures of the…

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随机区组实验中的删失观测AI 解读

SUMMARY Maximum likelihood methods are developed for the analysis of data from randomized block experiments, when some of the observations are censored. A modification of the maximum likelihood process, intended to produce approximately unbiased estimates of variance, is described, and the results of some numerical investigations into its efficacy are reported. Analogues of the t-test, using two alternative formulae for standard errors of differences, are considered, with…

具有两个不同状态的线性回归系统参数估计AI 解读

In attempting to estimate the parameters of a linear regression system obeying two separate regimes, it is necessary first to estimate the position of the point in time at which the switch from one regime to the other occurred. The suggested maximum likelihood estimating procedure is based upon a direct examination of the likelihood function. An asymptotic and a small-sample test are suggested for testing the hypothesis that no switch occurred against the single alternative…

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使用工具变量估计经济关系AI 解读

which the relationships are not exact, so that a set of ideal economic variables is assumed to be generated by a set of dynamic stochastic relationships, as in Koopmans [12], and the actual economic time series are assumed to differ from the ideal economic variables because of random disturbances or measurement errors. The asymptotic error variance matrix for the coefficients of one of the relationships is obtained in the case in which these relationships are estimated using…

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Normit 分析估计正态分布函数的表格：使用说明与估计方法比较AI 解读

JOSEPH BERKSON; TABLES FOR USE IN ESTIMATING THE NORMAL DISTRIBUTION FUNCTION BY NORMIT ANALYSIS: PART I. DESCRIPTION AND USE OF TABLES: PART II. COMPARISON BET

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正则马尔可夫链及某些随机游走中的充分性条件AI 解读

For positively regular Markov chains with a finite number of states, transition probabilities of the form are known to admit a sufficient estimator of θ in realizations of the chain starting with a fixed state and consisting of a fixed number of transitions. This paper considers whether transition probabilities of the same form will admit a sufficient estimator of θ in other finite regular, but not positively regular, Markov chains. For chains with an irreducible subset of…

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一类使最大似然估计在所有样本量下均无偏且方差最小的分布AI 解读

D. E. BARTON; A class of distributions for which the maximum-likelihood estimator is unbiased and of minimum variance for all sample sizes, Biometrika, Volume 4

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