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每层抽取两个单位时不等概率抽样估计量及方差估计量的稳定性研究AI 解读

Stabilities of estimators of the population total and stabilities of their variance estimators are compared for the following methods of sampling two units per stratum: (a) the I.P.P.S. (inclusion probabilities proportional to size) methods of Brewer, Fellegi and Hanurav using the Horvitz-Thompson estimator, (b) Des Raj's and Murthy's methods of p.p.s. sampling without replacement, (c) the Rao-Hartley-Cochran method, (d) Lahiri's method using a ratio estimator and (e) p.p.s.…

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似然实例及其与点估计和大样本近似的比较AI 解读

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…

多元统计中的缺失观测之四：简单线性回归札记AI 解读

In this note we examine the bias and small sample efficiency of certain estimators for the parameters of a linear regression function when some observations are missing. The estimators studies in this paper were suggested by the large sample study reported in this issue of the Journal. We conclude that our asymptotically unbiased estimators of β and μy | x have negligible bias in sample sizes as small as n = 20, and that our asymptotically unbiased estimator of σ2 may have…

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相关 Student t 随机变量之比的分布AI 解读

The distribution of the ratio of correlated Student t-variates is of interest in problems in econometrics, and ranking and selection. The density of this ratio is derived and computer graphs of the density are given in terms of standardized variates. Fractiles are given for selected parameter values. It is shown that the distribution contains no moments.

LAMST与列联表无三因素交互作用假设AI 解读

A new class of tests is presented for testing the hypothesis of no second order interaction in three-way contingency tables. This hypothesis is expressed first in the form of linear contrasts in logarithms of the parameters of a multinomial experiment and the test is based on the general theory of locally asymptotically most stringent tests. Specific test criteria are then given for testing no second order interaction in 2 × 2 × 2, 2 × 2 × K and I × J × K contingency tables.…

生物测定中的多样本升降法AI 解读

The up-and-down method in bioassay using multiple samples in each trial is investigated. The bias and precision of the estimators for ED 50 applying the dose-averaging formula and probit analysis are computed and relatively efficient sampling schemes are discussed. The use of the method to estimate extreme percentage doses is developed. It is shown that the estimators from this method are generally more efficient than the non-sequential estimators and are as good as other…

人口动态矩阵模型的若干随机版本AI 解读

In an effort to provide probabilistic measures of the accuracy of population projections, stochastic models for population growth are defined from the classical discrete deterministic model by assuming respectively that (1) the deterministic model is subject to additive random errors; (2) the elements of the transition matrix represent probabilities, rather than rates; and (3) the transition matrices are random variables. The mean of each process is shown to reproduce the…

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同一批个体上测得的相关系数AI 解读

When two correlation coefficients are calculated from a single sample, rather than from two samples, they are not statistically independent, and the usual methods for testing equality of the population correlation coefficients no longer apply. This paper considers the situation when the sample is from a multivariate normal distribution. Several possible large sample testing procedures are given, all based on Fisher's z-transformation. Power curves are given for each…

多元统计中的缺失观测（三）：简单线性回归的大样本分析AI 解读

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…

一类二元卡方分布的不等式AI 解读

The inequality is shown to hold when the joint distribution of U 1 and U 2 is a member of a class of bivariate Chi-Square distributions given. The relevance of this result to the construction of two-sided simultaneous confidence intervals for variances is noted.

方差的同时置信区间AI 解读

Given a sample of n vector observations from a multivariate normal population, Anderson and Roy-Gnanadesikan have given for the variances a set of confidence intervals which are approximate in that a lower bound only is known for the joint confidence coefficient. In the present study, exact procedures are developed in terms of multivariate Chi-Square distributions, and more general approximate procedures are given via Bonferroni's inequality. A numerical investigation…

一种新的异方差检验AI 解读

The quite general test for heteroskedasticity presented here regresses the absolute values of the residuals obtained by ordinary least-squares on some variable(s). Denoting the O.L.S. residuals by , one obtains, for instance, a regression like where z is a variable, a and b regression coefficients and the residuals of the new regression. We call the acceptance of a non-zero value for both a and b a case of “mixed heteroskedasticity”, which we deem frequent in practice though…

多元分布中线性次序统计量的渐近联合分布AI 解读

The asymptotic joint distribution of an arbitrary number of linear systematic statistics (that is, linear combinations of order statistics), when observations are made on a random vector, is shown to be normal under fairly general conditions. The linear systematic statistics may correspond to the same or to different components of the vector. Formulas for evaluating the parameters of the asymptotic normal distribution are derived. As an illustration, these are applied to the…

已知方差的多个正态总体最大均值的区间估计AI 解读

A procedure is given for the construction of a fixed-width confidence interval of the largest mean of k(k≥1) normal populations with a common known variance, based on the largest sample mean. The sample size required to achieve the preassigned confidence coefficient can be computed by using the standard normal table only.

动态计量经济模型的均衡协方差矩阵AI 解读

This paper presents a convenient form for the asymptotic, or equilibrium, covariance matrix of the endogenous variable vector of a dynamic econometric model.

关于 Theil 混合回归估计量AI 解读

Theil [4] obtained an estimator for a regression coefficient by combining sample information with stochastic a priori information which might be available on some or all the elements of the regression coefficient vector. Finite sample properties of this estimator are studied here.

自相关误差下若干两阶段回归方法的小样本性质AI 解读

In a linear regression model, when errors are autocorrelated, several asymptotically efficient estimators of parameters have been suggested in the literature. In this paper we study their small sample efficiency using Monte Carlo methods. While none of these estimators turns out to be distinctly superior to the others over the entire range of parameters, there is a definite gain in efficiency to be had from using some two-stage procedure in the presence of moderate high…

复合多项分布与有限总体分类数据的贝叶斯分析AI 解读

A Bayesian analysis of the parameter vector, W (Wj = number of elements in category j), of a multivariate hypergeometric distribution is considered. It is shown that if, a priori, W is compound multinomial (CMtn), then, a posteriori, W is a translated CMtn. Many properties of the CMtn distribution are derived. These include joint moments of all orders; a characterization in terms of independent compound Poisson variables, conditional distribution of one subvector given…

印度储蓄行为的计量探索AI 解读

The purpose of the study is to throw some light on the saving behavior of urban Indian households. The nature of the effects on saving of income and net worth and their interactions are examined in detail for different socio-economic sub-groups. There is strong evidence that income and net worth significantly influence the level of saving. Contrary to the studies in advanced countries, home-owners had a much lower saving-income ratio than renters although the former had a…