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含大型单位的简单随机样本下总体总量的若干估计量AI 解读

The problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators that…

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一般Gauss–Markov线性模型的约束最小二乘方法AI 解读

The task of estimating the vector of parameters β in the general Gauss-Markov model (y, Xβ, σ2 W) with no restrictions on the design matrix X or the covariance matrix σ2 W is formulated as a constrained linear least squares problem. A BLUE of any estimable function of β is obtained directly by solving this problem. The use of matrix decompositions leads to numerically stable algorithms for computing the solution. The approach is theoretically easy and is shown to be…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

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学生化极差检验的一个多元对应形式AI 解读

It is well known that T max 2 test procedure, a multivariate analog of studentized range test, can be derived by using Roy's union intersection principle with a bilinear decomposition of the MANOVA hypothesis that is response-wise infinite and contrastwise finite. In this article an alternative union intersection derivation of T max 2 test is presented using the matrix decomposition of the MAN-OVA hypothesis. This decomposition is responsewise as well as contrastwise…

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序贯概率比检验停止时间的方差与高阶中心矩札记AI 解读

Results are obtained on the limiting distribution and corresponding moment convergence for the (normalized) stopping time of an SPRT, as the boundaries of the continuation region become infinite. These asymptotic results suggest a certain approximation for the variance of the stopping time, which is compared with some Monte Carlo results of Cox and Roseberry (1966) and an approximation due to Ghosh (1969), in the case of testing a normal mean with known variance. The…

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分位数区间内外置信区间的置信系数界AI 解读

In this article, bounds for the confidence coefficients of outer and inner confidence intervals for quantile intervals are obtained using properties of convex functions. The bounds obtained here are sharper than the bounds given in Krewski (1976) and Reiss and Ruschendorf (1976).

基于有序观测的指数平均寿命不变序贯估计AI 解读

This paper derives the best invariant sequential estimate of exponential mean life for the situation where observations become available sequentially. If a cost function proportional to the observed time and relative squared error loss are adopted, it turns out that the best invariant rule is a fixed sample size rule.

计算机随机变量生成中接受—拒绝方法的一种变体AI 解读

A variant of the common acceptance-rejection method for generating random variables guarantees that steps are not repeated. This approach affords considerable flexibility in tailoring the method efficiently to the specified density. An algorithm for generating Cauchy random variables illustrates the use of this approach.

九种有限总体均值两阶段比率估计量的效率AI 解读

Nine two-phase ratio estimators for the mean of a finite population are presented. Assuming a linear model, exact expressions for their biases and mean squared errors are derived. Then the nine estimators are compared as to bias and mean squared error. The list of estimators includes the Jackknife estimator and four modifications; two of the proposed modifications are implemented by first expressing the classical estimator in the form of a regression estimator.

用于统计推断的若干傅里叶方法AI 解读

Common statistical procedures such as maximum likelihood and M-estimation admit generalized representations in the Fourier domain. The Fourier domain provides fertile ground for approaching a number of difficult problems in inference. In particular, the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain…

离散程度矩阵与主成分的稳健估计AI 解读

This paper uses Monte Carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components. The estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and M-estimation. The M-estimators stand up exceptionally well. They and the multivariate trimming procedure are especially effective at estimating the…

复杂抽样分类数据分析：拟合优度与二维表独立性的卡方检验AI 解读

The effect of stratification and clustering on the asymptotic distributions of standard Pearson chi-squared test statistics for goodness of fit (simple hypothesis) and independence in a two-way contingency table, denoted as X 2 and XI 2, respectively, is investigated. It is shown that both X 2 and XI 2 are asymptotically distributed as weighted sums of independent χ1 2 random variables. The weights are then related to the familiar design effects (deffs) used by survey…

非正态总体下样本方差分布的高斯近似AI 解读

A Gaussian approximation to the distribution of the sample variance is developed using the Wilson-Hilferty (1931) approach. This approximation is compared with the well-known approximations due to Box (1953), Roy and Tiku (1962), and Tan and Wong (1977) by taking the exponential, Laplace, uniform, product normal, Weibull, lognormal, Tine, logistic, and various mixtures of normal distributions as parent populations. The Gaussian approximation, which can be used for…

改进有限信息最大似然估计量分布的渐近展开AI 解读

An improvement of the limited information maximum likelihood (LIML) estimator was proposed by Morimune (1978). In this note two asymptotic expansions of the distribution of the improved estimator are derived, both for large sample size and for large values of the noncentrality parameter. The improved estimator uniformly dominates the LIML estimator in terms of the probability of concentration around the true coefficient for both the parameter sequences. The distributions of…

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