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不完整数据下的参数估计AI 解读

THE present note is concerned with a special case of the general problem of obtaining efficient estimators for the parameters of a normal multivariate population when the available sample data are incomplete in the sense that measures on all variables are not available for all individuals in the sample. Such fragmentary data may arise because part of the data are irretrievably lost (e.g., in an archaeological find), or because certain data were purposely not collected. The…

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支持范围依赖参数且存在充分统计量时的参数置信区间AI 解读

Summary This paper gives the sampling distribution of a sufficient statistic (which is also the maximum likelihood statistic) for the parameter of a distribution when the range of the distribution depends upon the parameter. Confidence intervals for the parameter are obtained, based on the distribution of the sufficient statistic.

两种处理的定性反应实验分析中变换与最大似然法的应用AI 解读

F. YATES, F. R. S.; THE USE OF TRANSFORMATIONS AND MAXIMUM LIKELIHOOD IN THE ANALYSIS OF QUANTAL EXPERIMIENTS INVOLVING TWO TREATMENTS, Biometrika, Volume 42, I

简单马尔可夫链未知参数最大似然估计的定理与充分性条件AI 解读

The paper begins with proofs of the usual theorems for the optimum properties of the maximum-likelihood estimator of an unknown parameter θ which defines the transition probabilities pij(θ) of a simple ergodic Markov chain. By an ergodic chain is meant one for which, not only is the final chain stationary, but also all possible initial states remain permanently available; these conditions are sufficient to prove that the maximum-likelihood estimator is consistent, and…

凹函数纵坐标的点估计AI 解读

A method is developed for obtaining maximum likelihood estimates of points on a surface of unspecified algebraic form when ordinates of the points are required to satisfy a set of linear inequalities. A production function with one variable input is considered in some detail. In this case the restrictions follow from the assumption of non-increasing returns. An illustrative computation is worked out using a procedure based on equivalence between the estimation problem and a…

截断样本与删失样本中的泊松参数估计AI 解读

Maximum likelihood estimators of the Poisson parameter applicable to both truncated and censored samples are derived in this paper. Singly and doubly truncated samples as well as singly and doubly censored samples are considered. The estimators obtained are presented in simple algebraic forms and their application to practical problems with the aid of standard Poisson tables is illustrated with numerical examples. Asymptotic variances of estimates for the different cases…

由截断样本估计Ⅲ型总体的参数AI 解读

The problem considered is the estimation of the mean and variance of Type III populations from singly and doubly truncated samples with known truncation points when the number of unmeasured observations is (i) unknown for each tail, (ii) known separately for each tail, (iii) known jointly for the two tails. For singly truncated samples, estimation of all three parameters has also been considered. Estimating equations are obtained by the method of moments as well as by the…

不放回抽样下总体中特定特征人数的置信区间AI 解读

IN A number of different sampling situations, we encounter a problem which may be stated as follows: From a population of N objects, each of which possesses or does not possess a certain characteristic, we select without replacement a random sample of n objects. Observing that m of these possess the characteristic in question, we wish to estimate the total number M having the property. This problem arises in sample surveys of human populations and in sampling inspection of…

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统计分析中的主观判断：一项实验研究AI 解读

Summary As part of an experimental study of the effect of stopping iterative maximum likelihood calculations after one cycle, twenty-one scientists were asked to judge by eye the positions for a pair of parallel probit regression lines in a biological assay. This paper reports the results obtained from each pair of lines after one cycle of various forms of probit calculation. Although all the conditions of the experiment were chosen so as to be unfavourable to the drawing of…

三参数对数正态分布的最大似然参数估计AI 解读

This paper is concerned with the three-parameter logarithmic normal distribution; i.e., the general distribution in which the terminus is unknown. Maximum likelihood equations for estimating population parameters from random samples are derived, and an iterative method for their solution is outlined. Variances and covariances of these estimates are obtained from the information matrix. An illustrative example is included.

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利用捕获—再捕获数据估计种群参数AI 解读

P. H. LESLIE, DENNIS CHITTY; THE ESTIMATION OF POPULATION PARAMETERS FROM DATA OBTAINED BY MEANS OF THE CAPTURE-RECAPTUTRE METHOD: THE MAXIMUM LIKELIHOOD E

极大似然法计算剂量反应曲线的若干新方面AI 解读

The estimation of the parameters of dosage response curves by the standard probit method is an iterative process beginning with approximations to the parameters and using one or more cycles of computations to “improve” these estimates until they converge. The present paper gives a table and method for computing the maximum likelihood solution which converges more rapidly than the standard probit method. A procedure is presented for obtaining more accurate initial…

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以线性变换求最小卡方与最大似然解：侧重生物测定AI 解读

An old and commonly used device for fitting a curve y = F(x, α, β) is to find a function of y which is linearly related to x, or a function of x which is linearly related to y, or functions of y and x which are linearly related to each other. The linearly related functions are plotted against one another, and a line is fitted to the points, usually by eye, sometimes by “least squares” in terms of the transforms. Texts dealing with empirical curve-fitting characteristically…

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关于一种最大似然估计的札记AI 解读

An estimate of y obtained by applying the method of maximum likelihood under the assumption that ut is normally distributed is consistent and asymptotically normally distributed. The asymptotic standard deviation is given in this note. Although Kendall considers many estimates of the period in his publication, he does not use the maximum-likelihood estimate although it has desirable properties in large samples that several of the other estimates do not have.4 It is…

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