Estimation of the parameter in the problem of the nile

Estimation of the parameter in the problem of the Nile is treated as a decision problem with squared error loss, It is shown that the minimum risk scale equivariant estimator dominates the incomplete sufficient unbiased estimators considered by Iwase and Seto, Sharper bounds for the equivariant estimator are derived which may be used to obtain the values of the same from the sample with sufficient accuracy.     

On the Computation of the Distribution for the Analysis of Means

Abstract

We discuss the accuracy of the computation and present a fortran program to compute the cumulative distribution function (CDF) for the analysis of means (ANOM).     

Evaluating the power of the mann-whitney test using the bootstrap method

In this paper we evaluate the power of the Mann-Whitney test in the shift model G(x) = F (x+θ) for all x , where the distribution of G is obtained by shifting F by an amount of θ.

The bootstrap method was used to evaluate the power of the Mann-Whitney test . A comparison among the bootstrap power , the asymptotic power of the Mann-Whitney test and the t-test power proved that the bootstrap is a better technique , because , it does not require the assumption of normality.     

Transforming the exponential by minimizing the sum of the absolute differences

This work presents an optimal value to be used in the power transformation to transform the exponential to normality for statistical process control (SPC) applications. The optimal value is found by minimizing the sum of absolute differences between two distinct cumulative probability functions. Based on this criterion, a numerical search yields a proposed value of 3.5142, so the transformed distribution is well approximated by the normal distribution. Two examples are presented to demonstrate the effectiveness of using the transformation method and its applications in SPC. The transformed data are almost normally distributed and the performance of the individual charts is satisfactory. Compared to charts that use the original exponential data and probability control limits, the individual charts constructed using the transformed distribution are superior in appearance, ease of interpretation and implementation by practitioners.     

On the estimation of the parameters of the von mises distribution

The usual maximum likelihood estimators of the parameters of the von Mises distribution are shown to perform badly in small samples. In view of this and the fact that these estimators require a large amount of computation, alternative, simpler estimators are proposed. It is shown that these estimators are at least comparable to the traditional estimators and are, in many cases, superior to them. We also apply the procedure of jackknifing to the maximum likelihood estimator of the concentration parameter of the von Mises distribution and compare the properties of the jackknifed estimator with the other estimators considered in this paper.     

On the robustness of the power function of the one-sample test for the negative exponential distribution

The robustness of the power function of the standard one-sample parametric test for the mean of the negative exponential distribution is examined. The main form of departure from the exponential assumption is a mixture of negative exponential components although an alternative Gamma distribution is also examined. It is found that the test is sensitive to these departures although the effect of mixtures with short tails is less dramatic than those with long tails.     

Calculating the mvue of the fraction nonconforming for the bivariate normal

The minimum variance unbiased estimator of the proportion lying outside an m-dimensional rectangle for multivariate normal populations was derived by Baillie (1987a, b). The estimator is a natural extension of a univariate estimator widely used in acceptance sampling. Computation of the multivariate estimator is nontrivial; one must integrate a multivariate density over the intersection of an m-dimensional ellipsoid and an m-dimensional rectangle. We propose an algorithm for the bivariate case which involves a one-dimensional numerical integration and calls to routines for either an incomplete beta function or a Student's t cumulative distribution function     

论国民经济核算体系的理论基础

国民经济核算体系是宏观经济管理的重要工具,它在经济研究的领域中正受到世界各国越来越多的注意。国民经济核算体系首先是经济理论与经济统计相结合的产物,正确地理解核算体系的理论基础,对于核算体系的研究是十分重要的。     

On the experience of projecting the family composition of the population of the USSR

The joint efforts in the USSR by the Central Planning Commission and the State Statistical Commission to develop projections of family characteristics of the Soviet population are described. The projections, based on official data for the rural and urban populations in 1987, are for the years 1991, 1996, 2001, and 2006.     

经济体制改革与统计工作改革

党的十二届三中全会通过的《中共中央关于经济体制改革的决定》,正确地总结了历史和现实的经验教训,提出和阐明了经济体制改革的一系列重大理论和方针政策。它对指导我国以城市为重点的整个经济体制改革,对指导我国统计工作改革,都具有重要的理论意义和实践意义。     

人工神经网络变量选取与隐藏单元数的确定

根据多隐藏层所有训练样本误差平方和最小设计优化问题,求解并绘出计算流程图。Trevor等人认为隐藏单元过多比过少好,交叉验证估计（隐藏单元）正则化参数没有必要。还有一种通常做法是常常利用分类树挑选变量作为输入变量进行人工神经网络建模。而从人工神经网络与多元统计、传统回归和其他数据挖掘工具的区别和联系出发,认为这些观点和做法值得商酌;用ZIP编码实例说明隐藏单元过多不一定比过少好,实际数据分析中所需隐藏单元数的确定可以用交叉验证结合经验判断来实现,利用分类树选择的变量对于人工神经网络没有太大的效果;通过分类树删节变量以降低计算量的效果不如通过压缩隐藏单元个数降低计算量来得好;非完全问题“从简单到一般”思想与完全问题中选择所有变量的思想不矛盾。在总结了Le Cun等人的局部联结以有效降低权数思想的基础上,提出通过随机选择人工变量建立人工神经网络分布式模型系统的设想。     

On the UMVU estimator for the generalized variance of the multinomial family

Abstract

The generalized variance is an important statistical indicator which appears in a number of statistical topics. It is a successful measure for multivariate data concentration. In this article, we established, in a closed form, the bias of the generalized variance maximum likelihood estimator of the Multinomial family. We also derived, with a complete proof, the uniformly minimum variance unbiased estimator (UMVU) for the generalized variance of this family. These results rely on explicit calculations, the completeness of the exponential family and the Lehmann–Scheffé theorem.     

On the distributions of the differences between the estimated autocorrelations and partial autocorrelations at the same lag

Pukkila (1982) introduced a new portmanteau-type test of white noise. The test is based on the differences between the estimated autocorrelations and the corresponding partial autocorrelations. In the present paper the distributions of these differences are consider in the case of normal white noise. Approximations to these distributions are given. Goodness of fit of these theoretical distributions and the corresponding observed distributions is studied using simulated time series of various lengths.     

On the adequacy of the chi-squared approximation for the coefficient of variation

The X² approximation to the distribution of the sample coefficient of variation of a normally distributed random variable, due to McKay 1932 is not nearly as accurate as suggested by the confirmatory studies of Fieller 1932 and Pearson 1932.The approximation will, however, be adequate in many practical situations and has the convenience of requiring nothing more than the readily available tables of x².     

On the estimates of the parameters of the first order autoregressive process

Two methods of estimation for the parameters of an AR(1) process which are based on a non-linear least-squares approach are presented. On the basis of some simulation results they are compared with two maximum likelihood estimates and their relative merits are discussed.     

On the performance of the poisson and the negative binomial ridge predictors

Mansson and Shukur (2011 Mansson, K., Shukur, G. (2011). A Poisson ridge regression estimator. Economic Modelling 28:1475–1481. [Google Scholar]) investigated the performance of the Poisson ridge regression (PRR) estimator in terms of the mean square error (MSE) criterion. Similarly, Mansson (2012 Mansson, K. (2012). On ridge estimators for the negative binomial regression model. Economic Modelling 29:178–184. [Google Scholar]) investigated the performance of the Negative binomial ridge regression (NBRR) according to the MSE criterion. But there is no any analysis of the predictive performance of the PRR and NBRR estimators. Therefore, we define the PRR and the NBRR predictors to evaluate their predictive performances according to the prediction mean squared error under the target function. The Monte Carlo simulations and the real life numerical example are conducted to investigate the defined predictors' performance.     

On the validity of the indeterminate latent variables in the lisrel model

The language of abstract vector spaces is used to show that the latent variables and errors of the Lisrel model can always be constructed so as to predict any criterion perfectly,including all those that are entirely uncorrelated with the observed variables.     

On the quantile past lifetime of the components of the parallel systems

ABSTRACT

Let T_{1: n} ? T_{2: n} ? ??? ? T_{n: n} be ordered lifetimes of components of a parallel system. In this article, the α-quantile past lifetime from the failure of the component with lifetime T_{r: n} provided that the system has failed at or before time t has been introduced. Then, some properties of this measure have been studied.