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分组样本中用于估计与假设检验的一致统计量AI 解读

This paper deals with the problem of making statistical inferences about an unknown parameter in the case when the smaple is grouped at the mid-points of equispaced intervals. The main discussion is concerned with a method which leads to consistent statistics, and with the asymptotic efficiency of these statistics compared to (a) the same statistics with ungrouped data, and (b) the maximum likelihood statistics. Unlike previous corrections or grouping, due to Sheppard and…

Neyman A型分布的二元推广AI 解读

Three generalizations of the Neyman Type A distribution (Neyman, 1939) to the bivariate case are introduced, each of which is such that each of its marginal distributions is univariate Neyman A. The models from which they arise seem appropriate in certain ecological situations. Method of moments estimators of the parameters are derived, and an example is given of an attempt to fit the three distributions to ecological data. The problems of maximum-likelihood estimation and…

单侧与双侧删失样本下正态总体参数的迭代极大似然估计AI 解读

SUMMARY Iterative procedures are given for joint maximum-likelihood estimation based on singly and doubly censored samples from a normal population. The simultaneous equations yielding the maximum-likelihood estimates are obtained. Since their algebraic solution is impossible, iterative procedures are proposed which are applicable in the most general case in which both parameters are unknown and in special cases in which either of the parameters is known. The asymptotic…

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同时存在死亡与迁入的捕获—再捕获数据显式估计：随机模型AI 解读

A brief review, with references, of the literature on capture-recapture theory is given in Jolly (1963). More recently, Cormack (1964) gives a solution, including asymptotic variances, for a specific situation involving the marking and release of a non-random sample of fulmar petrels. His model is stochastic and will be referred to in ? 4. Seber (1962, 1965) has also produced some interesting solutions, and these together with Darroch (1958, 1959) are most directly relevant…

吸收马尔可夫链中的若干统计推断问题AI 解读

The estimation of parameters in an absorbing Markov chain has been discussed by Gani (1956), Bhat & Gani (1960), Bhat (1961) and possibly by other authors. Asymptotic theory for the distribution of maximum-likelihood estimators applies if a large number of independent replicates of the chain is available. These replicates, however, could be considered as occurring sequentially in time, so that the chain has implicitly been altered in such a way that the absorbing state has…

单参数指数模型的估计AI 解读

An estimation procedure, called the “partial totals” method, is presented, illustrated and evaluated for the model y = exp(-pt)+e when the values of t are equally spaced. Tables of estimates using this estimation procedure are given for the case where the smallest value of t is zero. The evaluation consists of an analytical investigation of the large sample properties of the partial totals estimator and a report on a comparative study of its small sample properties relative…

线性结构关系的极大似然估计札记AI 解读

It is shown that the maximum likelihood estimate of a structural relationship line with uncorrelated errors is usually the same when both error variances are known as when only the ratio is known though exceptionally the slope of the line may be indeterminate. It is also shown how the equations given by Madansky [2] for the maximum likelihood estimates in the case when one error variance is known needs to be modified when, under certain circumstances, they are inconsistent.

A natural generalization of least squares is proposed to estimate parameters in simultaneous linear equations. Full-information maximum likelihood is shown to be identical with this generalization. The extent to which other estimators deviate from the generalization is discussed. A paradox of Strotz is resolved, and application of canonical correlation theory to structural equations is indicated. 1. SUMMARY THIS PAPER compares various estimators of the parameters of linear…

两个多项式回归交点的估计AI 解读

Let t* denote an unknown abscissa of intersection of two true regression functions μ1(t) and μ2(t). Under normality assumptions with no restraints on t* the maximum likelihood estimator of t* is shown to be the corresponding intersection of the sample regressions. When this estimate exists confidence intervals J can usually be obtained for t* by an application of the Student t-distribution. When t* is restrained to some known interval I, the ML estimate may or may not fall…

局部条件充分性AI 解读

Summary The concept of sufficiency can be examined locally for a neighbourhood of a parameter point θ0 and it leads to an estimate that has minimum variance among locally-unbiased estimates (Fraser, 1964). This local estimate generates the natural global estimate for the case of the simple exponential model, but it does not do so for the important case of the general translation model. The global estimate, the Pitman estimate, for this translation model is rooted in…

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最大似然估计量的高阶矩AI 解读

SUMMARY For a distribution depending on a single parameter the first four sampling moments of the maximum-likelihood estimate to orders N−2, N−3, N−3 and N−4 respectively are given. Expressions for the measures of skewness γ1 and γ2 are also given. Several illustrative examples are included as a check on the heavy algebra. The paper extends earlier work by Haldane and Smith.

截断二元正态分布的参数估计AI 解读

Estimates of parameters of a singly truncated bivariate normal distribution have been directly obtained using eight (or nine) moments. Asymptotic variances and covariances of these estimates are given and they are compared with those of maximum likelihood estimates.

单侧截断二元正态分布的参数估计AI 解读

Estimates of parameters of a singly truncated bivariate normal distribution have been directly obtained using eight (or nine) moments. Asymptotic variances and covariances of these estimates are given and they are compared with those of maximum likelihood estimates.

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利用最小次序对比平方估计误差方差AI 解读

Tables are given to facilitate the maximum likelihood estimation of error variance using the M smallest squares of K single degree of freedom contrasts. Some statistical properties of the estimate based on a random sampling experiment are given.

关于 Richards 所提最大似然估计方法的若干说明AI 解读

SUMMARY Richards (1961) suggested a method of maximum-likelihood estimation for the case of several parameters. Some gaps in the general theory given by him in support of the method are pointed out. Though the method is justifiable, the justification is shown to depend on the correct use of the implicit function theorem and is not connected with the joint asymptotic normality and the asymptotic efficiency of the maximum-likelihood estimates.

短马尔可夫序列的参数估计AI 解读

SUMMARY A parametric representation of a two-state Markov process is given which enables the maximum-likelihood estimates of the two parameters to be found without iteration.

三维列联表中的最大似然估计AI 解读

SUMMARY Interactions in three-way and many-way contingency tables are defined as certain linear combinations of the logarithms of the expected frequencies. Maximum-likelihood estimation is discussed for many-way tables and the solutions given for three-way tables in the cases of greatest interest.

杂论：利用次序统计量分别极大似然估计伽马分布的尺度或形状参数AI 解读

M. B. WILK, R. GNANADESIKAN, MARILYN J. HUYETT; Miscellanea: Separate maximum likelihood estimation of scale or shape parameters of the gamma distribution

边际消费倾向的最小二乘与最大似然估计量的精确抽样分布AI 解读

In this article we derive the exact finite sample frequency functions of the least squares and maximum likelihood estimators of the marginal propensity to consume, assuming the basic stochastic Keynesian model. The properties of these functions are considered in more detail for particular values of the parameters and sizes of sample. It is concluded that, for samples of 10 or more observations, generated by the model considered (with realistic values of the parameters), the…

两个正态总体参数的联合估计AI 解读

The problem of estimating a common mean from two independent sample means often arises. This paper describes an iteration method of jointly estimating a common mean and the individual variances of two normal populations. These estimates are either the maximum likelihood estimates or differ only slightly from them.