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线性模型无偏估计的两种线性规划算法AI 解读

Consider the estimation of in the familiar linear model . It is well-known that the least squares estimation principle yields an un-biased estimator . Two alternative estimation principles sometimes considered are the minimization of the sum of absolute residuals and the minimization of the maximum absolute residual. Since these alternative principles do not usually lead to a unique estimator, the latter depends on the computational algorithm used. We develop two algorithms…

平方根估计量AI 解读

For certain skewed populations there are biased estimators of the population mean, , which have smaller mean square error than the sample mean . This article investigates the properties of the square-root estimator , where . It is shown that this estimator can provide substantial gains in efficiency over when sampling from highly skewed populations. Graphs and tables are presented showing optimum values of C for various types of distributions and sample sizes, and…

平方根估计量AI 解读

For certain skewed populations there are biased estimators of the population mean, , which have smaller mean square error than the sample mean . This article investigates the properties of the square-root estimator , where . It is shown that this estimator can provide substantial gains in efficiency over when sampling from highly skewed populations. Graphs and tables are presented showing optimum values of C for various types of distributions and sample sizes, and…

异方差线性模型的估计AI 解读

This article considers the familiar linear model in which the residual vector e has elements e i with expectation 0 but different variances σ2 i . The elements of and the σ2 i are estimated by maximum likelihood under the assumption of a lower bound for the σ2 i of the form 0 < δ2 i ≤ σ2 i so that the likelihood is finite in the restricted parameter space. A second problem is considered in which the y vector splits into k sub-vector y j , such that all elements of y j have…

用作拟合优度准则的次序统计量二次型AI 解读

Consider a sample vector, z, whosen elements z(i)are the probability transforms z(i) θ P{x(i)} of the order statistics x(i) of a random sample of size n drawn from a cumulative distribution function P(x). Most nonparametric goodness-of-fit criteria concerned with testing whether the specified P(x) is the true one are computed from z. The criterion considered here is the x2-type criterion S2 θ (z – μ)′V–1(z – μ), where μ θ E(z) and V θ E{(z –;μ)(z – μ)′}. The extract…

作为拟合优度准则的次序统计量二次型AI 解读

Consider a sample vector, z, whosen elements z(i)are the probability transforms z(i) θ P{x(i)} of the order statistics x(i) of a random sample of size n drawn from a cumulative distribution function P(x). Most nonparametric goodness-of-fit criteria concerned with testing whether the specified P(x) is the true one are computed from z. The criterion considered here is the x2-type criterion S2 θ (z – μ)′V–1(z – μ), where μ θ E(z) and V θ E{(z –;μ)(z – μ)′}. The extract…

每层仅抽取一个单位时的方差估计AI 解读

A new solution to the problem of variance estimation with one unit per stratum is presented. This method may lead to smaller bias in variance estimation, in many situations, than the methods of ‘collapsed strata’. It requires that we can associate with the strata concomitant variables which are correlated with the strata means. Several numerical examples with one or two concomitant variables are considered.

抽样调查的一种新估计理论AI 解读

A new estimation theory for sample surveys is proposed, the basic feature of which is a special parametrization of finite populations based on the assumptions that a character attached to the units is measured on a known scale with a finite set of scale points. In the class of estimators which do not functionally depend on the identification labels preattached to the units, the following results are proved: (1) For simple or stratified simple random sampling without…

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混合方差分析模型的最大似然估计AI 解读

A procedure is developed for the maximum-likelihood estimation of the unknown constants and variances included in the general mixed analysis of variance model, involving fixed and random factors and interactions. The method applies to all cases where the design matrices satisfy certain conditions. The consistency and asymptotic efficiency of the estimates are discussed. Tests of hypotheses and confidence regions are derived.

不等概率不放回系统抽样AI 解读

Given a population of N units, it is required to draw a sample of n distinct units in such a way that the probability for the i th unit to be in the sample is proportional to its ‘size’ x. From the alternative methods of achieving this we consider here only the so-called systematic method which, to the best of our knowledge, was first developed by W. G. Madow (1949): The units in the population are listed in a ‘particular’ order, their xi accumulated and a systematic…

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双向分层的设计与估计AI 解读

One may encounter populations for which there are two effective stratifying criteria, both of which are desirable in a sample design. However, the number of permitted observations may be less than the number of strata formed by the usual double stratification technique. A method which will permit estimation in these cases is presented. Both biased and unbiased estimators are considered. It is shown that if the stratification effects are additive in the analysis-of-variance…

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无偏比率型估计量的精度AI 解读

When each unit in a population of N units consists of an x and a y measurement, where the population mean [Xbar] of the x's is known, then the population mean [Ybar] of the y's is frequently estimated by drawing a random sample of n units and using one of the customary biased ratio-type estimators, [Ybar] (based on the ratio of the y sample mean and the x sample mean), or [Ybar] (based on the sample mean of the ratios of the y and x measurements for each unit). The precision…

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单个正态样本中极差与标准差之比的分布AI 解读

H. A. DAVID, H. O. HARTLEY, E. S. PEARSON; THE DISTRIBUTION OF THE RATIO, IN A SINGLE NORMAL SAMPLE, OF RANGE TO STANDARD DEVIATION, Biometrika, Volume 41,

系数随时间趋势变化的二阶自回归模型AI 解读

Summary It has been suggested that the departure of certain time series from a fitted second order autoregressive scheme is due to time-trending coefficients in the generating differential equation. If coefficients with linear time-trends are introduced into the scheme the correlogram of the resulting non-stationary series can, in special cases, be evaluated exactly in terms of Airy integrals and is found to be approximately of the form sin s/s where s is proportional to the…

由非中心 F 分布导出的方差分析检验功效图AI 解读

E. S. PEARSON, H. O. HARTLEY; CHARTS OF THE POWER FUNCTION FOR ANALYSIS OF VARIANCE TESTS, DERIVED FROM THE NON-CENTRAL F-DISTRIBUTION, Biometrika, Volume

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