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删失数据下生存概率的置信区间估计AI 解读

The likelihood ratio method for confidence interval estimation of survival or life-time probabilities is investigated for censored data. This approach depends on a constrained product-limit estimator for the survival function. The likelihood method is compared with two alternative methods based on normal approximations to the product-limit estimator for several cases of uncensored and randomly censored samples. The methods are generalized for the ratio of two survival…

卡方拟合优度检验准确性的另一种多项分布评估AI 解读

Tate and Hyer [9] indicated in a recent article that the χ2 test of goodness of fit is markedly in error when expected frequencies are small, and that, moreover, errors of substance remain even with large expected frequencies. This result appears to arise from the application of an improper statistical model. When the multinomial test proposed here is substituted, it is found that errors of the χ2 test are smaller than Tate and Hyer would suggest for small expected…

若干多样本非参数尺度检验的小样本表现AI 解读

Several nonparametric and parametric statistics for testing the equality of scale parameters are compared with respect to their power and stability of error rates. When the populations have mass confined to the positive axis, the c-sample analog of the sum of squared ranks test and the Kruskal-Wallis test are found to be very robust and powerful. When the populations are symmetrical, the c-sample analogs of the two-sample Mood and two-sample Ansari-Bradley tests are robust…

同时使用二元变量与连续变量的判别和分类AI 解读

The likelihood ratio classification rule is derived from the location model, applicable when the data contains both binary and continuous variables. A method is proposed for estimating the rule in practical situations and assessing its performance. Losses incurred by the estimation procedure are investigated, and use of Fisher's linear discriminant function on such data is studied for the case of known population parameters. Finally, the proposed rule is applied to some data…

多重共线性情形下的定向岭回归技术AI 解读

In the presence of multicollinearity ridge regression techniques result in estimated coefficients that are biased but have a smaller variance than ordinary least squares (OLS) estimators and may, therefore, have a smaller mean square error. The directed ridge estimator (DRE) suggested here alters only diagonal elements corresponding to relatively small eigenvalues. The advantage of our method is that the resulting estimates may be less biased than in other ridge regression…

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管理与经济学统计AI 解读

What is Statistics? Describing Sets of Measurements Probability Random Variables and Probability Distributions Three Useful Discrete Probability Distributions The Normal and Other Continuous Probability Distributions Sampling and Sampling Distributions Large sample Estimation Large Sample Tests of Hypotheses Inferences from Small Samples The Analysis of Variance Linear Regression and Correlation Multiple Linear Regression Elements of Time Series Analysis Forecasting Models…

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分枝过程灭绝概率的保序估计AI 解读

Suppose X 1, X 2, ···, Xn is a random sample from a distribution which assigns all of its mass to the nonnegative integers. Let p j = P[X 1 = j]; j = 0, 1, ··· and let f(·) be the generating function of the sequence {p j }∞ j=0. An estimate of the smallest nonnegative root of f(s) = s which is based on isotonized estimates of p 0, p 1, ··· is considered. Results of a simulation study, almost sure convergence rates and the asymptotic distribution theory are discussed.

完整或删失样本下 Logistic 分布参数的简单线性估计AI 解读

Linear unbiased estimators which maintain high efficiency relative to the best linear unbiased estimators are proposed for the parameters of the logistic distribution. In the complete sample case, the estimators of location and scale are, respectively, a trimmed mean and the mean deviation about the sample median with an adjustment for bias. The same computational forms are applied to a Windsorized sample in the cases of symmetric and upper one-sided censoring.

含截距回归曲面的单侧同时置信界AI 解读

Exact one-sided simultaneous confidence bounds are obtained for general regression surfaces with intercepts and functionally independent regressors. For all values of the regressors, the distance from the regression surface to the one-sided bound is a fixed fraction (less than one) of the corresponding distance to the well-known Working-Hotelling-Scheffé two-sided bound. Tables are provided to facilitate the use of such one-sided bounds.

Pitman 位置估计量的小样本方差AI 解读

For three symmetric distributions and six sample sizes, this article presents estimates of the small-sample variance of Pitman's location-invariant and location-scale-invariant estimators of location. It then compares these two estimators and investigates the closeness of the Cramér-Rao bound when estimators are required to be invariant. Expressions of the form c/(n − d) prove quite effective in fitting variances of Pitman estimators, and d can be interpreted as the amount…

有限总体中的两阶段比率估计量AI 解读

Modified ratio estimators for the mean are proposed for the case in which the first- and second-phase samples are drawn without replacement and independent of each other. Conditions for these estimators to be more efficient than the classical estimator are investigated. Two methods for evaluating the expectation of the reciprocal of the number of distinct units are presented.

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城市增长与迁移的联立方程模型AI 解读

The objectives of this study are twofold. First, a simultaneous-equations model that takes into account the interactions between various economic aspects of urban growth and migration to and from urban areas is specified. Second, the model is estimated for two different time periods, 1950–60 and 1960–70, with the Standard Metropolitan Statistical Area as the basic urban geographic unit. Included among the jointly dependent variables are civilian labor force out-migration,…

若干多样本非参数尺度检验的小样本表现AI 解读

Several nonparametric and parametric statistics for testing the equality of scale parameters are compared with respect to their power and stability of error rates. When the populations have mass confined to the positive axis, the c-sample analog of the sum of squared ranks test and the Kruskal-Wallis test are found to be very robust and powerful. When the populations are symmetrical, the c-sample analogs of the two-sample Mood and two-sample Ansari-Bradley tests are robust…

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