Type a incomplete multi-response designs

Srivastava considered the problem of designing and analysis of incomplete multi-response experiments, The main characteristics of the analysis given by her are investigated and a general class of incomplete multiresponse designs (Type A) is obtained on the basis of these investigations.     

ANOVA for unbalanced data: Use Type II instead of Type III sums of squares

Methods for analyzing unbalanced factorial designs can be traced back to Yates (1934). Today, most major statistical programs perform, by default, unbalanced ANOVA based on Type III sums of squares (Yates's weighted squares of means). As criticized by Nelder and Lane (1995), this analysis is founded on unrealistic models—models with interactions, but without all corresponding main effects. The Type II analysis (Yates's method of fitting constants) is usually not preferred because of the underlying assumption of no interactions. This argument is, however, also founded on unrealistic models. Furthermore, by considering the power of the two methods, it is clear that Type II is preferable.     

Phase Type Distributions with Finite Support

This research is motivated by the fact that many random variables of practical interest have a finite support. For fixed a < b, we consider the distribution of a random variable X = (a + Ymod(b ? a)), where Y is a phase type (PH) random variable. We demonstrate that as we traverse for Y the entire set of PH distributions (or even any subset thereof like Coxian that is dense in the class of distributions on [0, ∞)), we obtain a class of matrix exponential distributions dense in (a, b). We call these Finite Support Phase Type Distributions (FSPH) of the first kind. A simple example shows that though dense, this class by itself is not very efficient for modeling; therefore, we introduce (and derive the EM algorithms for) two other classes of finite support phase type distributions (FSPH). The properties of denseness, connection to Markov chains, the EM algorithm, and ability to exploit matrix-based computations should all make these classes of distributions attractive not only for applied probability but also for a much wider variety of fields using statistical methodologies.     

一类扩展的投入产出模型

 内容提要：基于居民部门封闭的投入产出模型进行扩展,并将政府部门从最终需求列中转移出来,纳入到生产部门,列入投入产出表的第Ⅰ象限,政府部门所在的行是以货币形式表现的各部门（包括居民部门）的税收支付,政府部门所在的列是政府对各个部门的各种消费品和劳务的消费额,得到了扩展的局部闭投入产出模型,并在此模型的基础上得到了各种乘数。进一步将投资考虑进去得到动态投入产出扩展模型,使得国民经济各个生产部门、居民部门、政府部门成为一个完整的投入产出平衡体。     

浅论链型指数

本文介绍了近年在美国国民经济核算体系中使用的链型指数的编制方法,指出了它的优缺点及其应用的积极意义,并给出了在国内开展链型指数应用和研究的建议。     

Type I and Type II error rates in the last observation carried forward method under informative dropout

Dropout is a persistent problem for a longitudinal study. We exhibit the shortcomings of the last observation carried forward method. It produces biased estimates of change in an outcome from baseline to study endpoint under informative dropout. We developed a theoretical quantification of the effect of such bias on type I and type II error rates. We present results for a setup where a subject either completes the study or drops out during one particular interval, and also under the setup in which subjects could drop out at any time during the study. The type I error rate steadily increases when time to dropout decreases or the common sample size increases. The inflation in type I error rate can be substantially high when reasons for dropout in the two groups differ; when there is a large difference in dropout rates between the control and treatment groups and when the common sample size is large; even when dropout subjects have one or two fewer observations than the completers. Similar results are also observed for type II error rates. A study can have very low power when early recovered patients in the treatment group and worsening patients in the control group drop out even near the end of the study.     

Parameter estimation and prediction of order statistics for the Burr Type XII distribution with Type II censoring

This article deals with the statistical inference and prediction on Burr Type XII parameters based on Type II censored sample. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained in closed form. We use the expectation-maximization algorithm to compute the MLEs. We also obtain the Bayes estimators under symmetric and asymmetric loss functions such as squared error and Linex By applying Lindley's approximation and Markov chain Monte Carlo (MCMC) technique. Further, MCMC samples are used to calculate the highest posterior density credible intervals. Monte Carlo simulation study and two real-life data-sets are presented to illustrate all of the methods developed here. Furthermore, we obtain a prediction of future order statistics based on the observed ordered because of its important application in different fields such as medical and engineering sciences. A numerical example carried out to illustrate the procedures obtained for prediction of future order statistics.     

Computing Probabilities of Type I Error and Type II Error of Sequential Bayesian Procedures for Testing One-Sided Hypotheses

In this article, it is shown how to compute, in an approximated way, probabilities of Type I error and Type II error of sequential Bayesian procedures for testing one-sided null hypotheses. First, some theoretical results are obtained, and then an algorithm is developed for applying these results. The prior predictive density plays a central role in this study.     

Bimatrix Variate Beta Type IV Distribution: Relation to Wilks's Statistic and Bimatrix Variate Kummer-Beta Type IV Distribution

In this article, the bimatrix variate beta Type IV distribution is derived from independent Wishart distributed matrix variables. We explore specific properties of this distribution which is then used to derive the exact expressions of the densities of the product and ratio of two dependent Wilks's statistics and to define the bimatrix Kummer-beta Type IV distribution.     

On the Bivariate Kummer-Beta Type IV Distribution

Recent studies have shown the X-bar control chart with variable sampling interval detects shifts in the process mean faster than the traditional X-bar chart. These studies are usually based on the assumption that the process data are independently and normally distributed. However, many situations in practice violate these assumptions. In this study, a methodology is developed to economically design a variable sampling interval X-bar control chart that takes into consideration correlated non normal sample data. An example is provided to illustrate the solution procedure. A sensitivity analysis on the input parameters (i.e., the cost and the process parameters) is performed taking into account the non normality and the correlation on the optimal design of the chart.     

Regression Type Estimators Using Multiple Auxiliary Information

In this paper we consider a practical situation where information on two auxiliary variables related to the study variable is available at different levels. Following Kiregyera (1980, 1984) who has obtained a chain ratio-to-regression estimator and regression to regression estimator, we shall study several estimators that arise naturally in this context and compare them under the mean square error criterion. We extend these results to the case when multiple auxiliary information is available.     

A formula for Type III sums of squares

Abstract

Type III methods were introduced by SAS to address difficulties in dummy-variable models for effects of multiple factors and covariates. They are widely used in practice; they are the default method in several statistical computing packages. Type III sums of squares (SSs) are defined by a set of instructions; an explicit mathematical formulation does not seem to exist.

An explicit formulation is derived in this paper. It is used to illustrate Type III SSs and to establish their properties in the two-factor ANOVA model.     

关于设计中国式投入产出表的问题

国务院决定进行全国1987年投入产出调查,编制1987年投入产出表。投入产出核算是国民经济核算体系中的重要组成部分。设计和编制全国投入产出表可有三种办法:第一种是在MPS投入产出表的基础上扩编为SNA投入产出表;第二种是直接编制SNA投入产出表,再转换为MPS投入产出表;第三种是设计一个非MPS,也非SNA的中国式的投入产出表。我们主张采用第三种办法,即在马克思主义理论指导下,从我国社会主义有计划商品经济的实际出发,以全部参与社会经济活动的部门为核算对象,大胆借鉴和运用MPS和SNA投入产     

Fisher Information in Type II Progressive Censored Samples

Recently, progressively Type II censored samples have attracted attention in the study and analysis of life-testing data. Here we propose an indirect approach for computing the Fisher information (FI) in progressively Type II censored samples that simplifies the calculations. Some recurrence relations for the FI in progressively Type II censored samples are derived that facilitate the FI computation using the proposed decomposition. This paper presents a standard recurrence relation that simplifies computation of the FI in progressively Type II censored samples to a sum; FI in collections order statistics (OS). We compute the FI in a collections of progressively Type II censored samples for some known distributions.     

A characterization of the Burr Type III and Type XII distributions through the method of percentiles and the Spearman correlation

A characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the method of (conventional) moments (MOM) in the context of estimation and fitting theoretical and empirical distributions. The methodology is based on simulating the Burr Type III and Type XII distributions with specified values of medians, inter-decile ranges, left-right tail-weight ratios, tail-weight factors, and Spearman correlations. Simulation results demonstrate that the MOP-based Burr Type III and Type XII distributions are substantially superior to their (conventional) MOM-based counterparts in terms of relative bias and relative efficiency.     

Matching Three Moments with Minimal Acyclic Phase Type Distributions

Abstract

A number of approximate analysis techniques are based on matching moments of continuous time phase type (PH) distributions. This paper presents an explicit method to compose minimal order continuous time acyclic phase type (APH) distributions with a given first three moments. To this end we also evaluate the bounds for the first three moments of order n APH distributions (APH(n)). The investigations of these properties are based on a basic transformation, which extends the APH(n ? 1) class with an additional phase in order to describe the APH(n) class.