基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。     

Robustness and Corrections for Sample Size Adaptation Strategies Based on Effect Size Estimation

A study on the robustness of the adaptation of the sample size for a phase III trial on the basis of existing phase II data is presented—when phase III is lower than phase II effect size. A criterion of clinical relevance for phase II results is applied in order to launch phase III, where data from phase II cannot be included in statistical analysis. The adaptation consists in adopting the conservative approach to sample size estimation, which takes into account the variability of phase II data. Some conservative sample size estimation strategies, Bayesian and frequentist, are compared with the calibrated optimal γ conservative strategy (viz. COS) which is the best performer when phase II and phase III effect sizes are equal. The Overall Power (OP) of these strategies and the mean square error (MSE) of their sample size estimators are computed under different scenarios, in the presence of the structural bias due to lower phase III effect size, for evaluating the robustness of the strategies. When the structural bias is quite small (i.e., the ratio of phase III to phase II effect size is greater than 0.8), and when some operating conditions for applying sample size estimation hold, COS can still provide acceptable results for planning phase III trials, even if in bias absence the OP was higher.

Main results concern the introduction of a correction, which affects just sample size estimates and not launch probabilities, for balancing the structural bias. In particular, the correction is based on a postulation of the structural bias; hence, it is more intuitive and easier to use than those based on the modification of Type I or/and Type II errors. A comparison of corrected conservative sample size estimation strategies is performed in the presence of a quite small bias. When the postulated correction is right, COS provides good OP and the lowest MSE. Moreover, the OPs of COS are even higher than those observed without bias, thanks to higher launch probability and a similar estimation performance. The structural bias can therefore be exploited for improving sample size estimation performances. When the postulated correction is smaller than necessary, COS is still the best performer, and it also works well. A higher than necessary correction should be avoided.     

Normal theory sample size formulas for some nonnormal distributions

Sample size procedures of T- and F-tests for some nonnormal distributions are discussed. An adaptation to the Kruskal-Wallis and Friedman tests is mentioned.     

Time series analysis for repeated surveys

Estimation of a characteristic based on surveys repeated at regular intervals is considered. A state space formulation is given for the problem and the Kalman Filter is used to obtain an estimate and its variance. Some examples are also given to illustrate the methodology.     

An Introduction to Ranking and Selection

This expository paper explains the philosophy of the indifference-zone approach and the subset-selection approach to ranking and selection procedures. It includes examples of operating characteristic curves and data applications for selection problems based on the binomial and normal distributions. A variety of different models and goals are provided with a list of references.     

The Use of Noncentral F Approximations for Calculation of Power and Sample Size

Approximations to the noncentral F distribution yield surprisingly accurate results for power and sample size problems arising from linear hypotheses about normal random variables. The approximations are easy to use with a desk (or hand-held) calculator that computes cumulative F probabilities. These approximations are particularly advantageous for testing the hypothesis that differences among the means are small against the alternative that the differences are large.     

The Sample Coefficient of Determination in Simple Linear Regression

The behavior of the sample coefficient of determination is examined for some arrangements of independent variable values in a simple linear regression with normally distributed error terms. Numerical values of means and standard deviations are presented that provide some insight into the influence of range and arrangement of independent variable values and sample size on the size of the sample coefficient of determination. Some asymptotic results are given.     

On Statistics Independent of a Sufficient Statistic: Basu's Lemma

The determination of optimal sample sizes for estimating the difference between population means to a desired degree of confidence and precision is a question of economic significance. This question, however, is generally not discussed in statistics texts. Sample sizes to minimize linear sampling costs are proportional to the population standard deviations and inversely proportional to the square roots of the unit sampling costs. Sensitivity analysis shows that the impact of the use of equal rather than optimal sample sizes on the amount of sampling and its cost is not great as long as the unit costs and population variances are comparable.     

An Interesting Property of the Sample Mean under a First-Order Autoregressive Model

The unweighted sample mean is examined as an estimator of the population mean in a first-order autoregressive model. It is demonstrated that the precision of this estimator deteriorates as the number of equally spaced observations taken within a fixed time interval increases.     

Fishery and Forestry Management

There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to adopt a standard definition for sample quantiles so that the same answers are produced by different packages and within each package. We conclude by recommending that the median-unbiased estimator be used because it has most of the desirable properties of a quantile estimator and can be defined independently of the underlying distribution.