Two new estimators of entropy for testing normality

ABSTRACT

We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the existing entropy estimators. Also, we propose two new tests for normality based on the introduced entropy estimators and compare their powers with the powers of other tests for normality. The results show that the proposed estimators and test statistics perform very well in estimating entropy and testing normality. A real example is presented and analyzed.     

Consistency of information criteria for model selection with missing data

ABSTRACT

In this paper, we investigate the consistency of the Expectation Maximization (EM) algorithm-based information criteria for model selection with missing data. The criteria correspond to a penalization of the conditional expectation of the complete data log-likelihood given the observed data and with respect to the missing data conditional density. We present asymptotic properties related to maximum likelihood estimation in the presence of incomplete data and we provide sufficient conditions for the consistency of model selection by minimizing the information criteria. Their finite sample performance is illustrated through simulation and real data studies.     

Optimal designs for estimating a choice hierarchy by a general nested multinomial logit model

Abstract

In choice experiments the process of decision-making can be more complex than the proposed by the Multinomial Logit Model (MNL). In these scenarios, models such as the Nested Multinomial Logit Model (NMNL) are often employed to model a more complex decision-making. Understanding the decision-making process is important in some fields such as marketing. Achieving a precise estimation of the models is crucial to the understanding of this process. To do this, optimal experimental designs are required. To construct an optimal design, information matrix is key. A previous research by others has developed the expression for the information matrix of the two-level NMNL model with two nests: Alternatives nest (J alternatives) and No-Choice nest (1 alternative). In this paper, we developed the likelihood function for a two-stage NMNL model for M nests and we present the expression for the information matrix for 2 nests with any amount of alternatives in them. We also show alternative D-optimal designs for No-Choice scenarios with similar relative efficiency but with less complex alternatives which can help to obtain more reliable answers and one application of these designs.     

Discrete adaptive design in attribute life testing

Properties of a discrete adaptive design in attribute life testing situation are studied. It is shown that the design is strongly consistent and asymptotically normal. Some examples are discussed to show that the design could be used in a wide range of ields, Finally, we give some simulation results to compare the discrete adaptive desigin with some continuous optimal designs.     

On the design of comparative lifetime studies

In designing a study to compare two lifetime distributions, decisions are required about the study size, the proportion of observations in each group and the length of follow-up period. These aspects of study design are examined using a Bayesian approach in which the expected consequences of a particular choice of design are evaluated by the expected gain in infornlation.     

我国行业分类与国际标准行业分类的比较研究

 本文通过对我国行业分类和国际标准行业分类两项分类标准最新版本的比较,对两项分类的基本构成、应用原则、门类和大类的条目结构以及对照转换等方面的情况进行了比较分析研究。详细解析了在若干行业领域中,二者存在典型差异的情况。最后,对我国的行业分类的科学性和国际可比性做出了分析评价,对如何进一步提升分类水平提出了改进意见,另外还提出了未来修订的思路和方法等建议。     

Optimal Designs for Binary Logistic Regression with a Qualitative Classifier with Independent Levels

Dose response studies arise in many medical applications. Often, such studies are considered within the framework of binary-response experiments such as success-failure. In such cases, popular choices for modeling the probability of response are logistic or probit models. Design optimality has been well studied for the logistic model with a continuous covariate. A natural extension of the logistic model is to consider the presence of a qualitative classifier. In this work, we explore D-, A-, and E-optimal designs in a two-parameter, binary logistic regression model after introducing a binary, qualitative classifier with independent levels.     

A Variable Selection Method for Analyzing Supersaturated Designs

Supersaturated designs are a large class of factorial designs which can be used for screening out the important factors from a large set of potentially active variables. The huge advantage of these designs is that they reduce the experimental cost drastically, but their critical disadvantage is the confounding involved in the statistical analysis. In this article, we propose a method for analyzing data using several types of supersaturated designs. Modifications of widely used information criteria are given and applied to the variable selection procedure for the identification of the active factors. The effectiveness of the proposed method is depicted via simulated experiments and comparisons.     

Analyzing Supersaturated Designs by Means of an Information Based Criterion

The cost and time consumption of many industrial experimentations can be reduced using the class of supersaturated designs since this can be used for screening out the important factors from a large set of potentially active variables. A supersaturated design is a design for which there are fewer runs than effects to be estimated. Although there exists a wide study of construction methods for supersaturated designs, their analysis methods are yet in an early research stage. In this article, we propose a method for analyzing data using a correlation-based measure, named as symmetrical uncertainty. This method combines measures from the information theory field and is used as the main idea of variable selection algorithms developed in data mining. In this work, the symmetrical uncertainty is used from another viewpoint in order to determine more directly the important factors. The specific method enables us to use supersaturated designs for analyzing data of generalized linear models for a Bernoulli response. We evaluate our method by using some of the existing supersaturated designs, obtained according to methods proposed by Tang and Wu (1997 Tang , B. , Wu , C. F. J. (1997). A method for constructing supersaturated designs and its E(s ²)-optimality. Canadian Journal of Statistics 25:191–201.[Crossref], [Web of Science ®] , [Google Scholar]) as well as by Koukouvinos et al. (2008 Koukouvinos , C. , Mylona , K. , Simos , D. E. ( 2008 ). E(s ²)-optimal and minimax-optimal cyclic supersaturated designs via multi-objective simulated annealing . Journal of Statistical Planning and Inference 138 : 1639 – 1646 .[Crossref], [Web of Science ®] , [Google Scholar]). The comparison is performed by some simulating experiments and the Type I and Type II error rates are calculated. Additionally, Receiver Operating Characteristics (ROC) curves methodology is applied as an additional statistical tool for performance evaluation.     

Simulated Distribution of the Kullback-Leibler Information Measure

This paper provides the percentiles obtained by simulation of an informational test statistic. It gives evidence that the widely used chi-square approximation to this test statistic is not suitable.