On generalized dynamic cumulative past entropy measure

Recently, the concept of dynamic cumulative residual entropy and its generalizations has gained much attention among researchers. In this work, a new generalized dynamic cumulative measure in the past lifetime is proposed. Further, some characterization results connecting this new generalized dynamic entropy measure and other reversed measures are obtained.     

A vector valued bivariate gini index for truncated distributions

Gini index is widely used in the study of inequality of income distribution. In the present paper we give a definition of the Gini index in the Bivariate set-up and look into the problem of characterizing probability distributions based on some relationship between this index and various other commonly used measures. We also generalized the Gini index to a situation where several attributes of the population are considered.     

Influence diagnostics in nonlinear reproductive dispersion mixed models

The class of nonlinear reproductive dispersion mixed models (NRDMMs) is an extension of nonlinear reproductive dispersion models and generalized linear mixed models. This paper discusses the influence analysis of the model based on Laplace approximation. The equivalence of case-deletion models and mean-shift outlier models in NRDMMs is investigated, and some diagnostic measures are proposed via the case-deletion method. We also investigate the assessment of local influence of various perturbation schemes. The proposed method is illustrated with an example.     

On generalized order statistics from generalized pareto distribution

The aim of this paper is to estimate parameters of generalized Pareto distribution based on generalized order statistics. Some non-Bayesian methods, such as MLE, bootstrap and unbiased estimators have been obtained to develop point and interval estimations. Bayesian estimations have also been derived under LSE and LINEX loss functions. To compare the performances of the employed methods, numerical results have been computed. To illustrate dependence and association properties of generalized order statistics, correlation coefficient and some informational measures in closed form have been obtained.     

The microeconometric estimation of treatment effects—An overview

Summary The need to evaluate the performance of active labour market policies is not questioned any longer. Even though OECD countries spend significant shares of national resources on these measures, unemployment rates remain high or even increase. We focus on microeconometric evaluation which has to solve the fundamental evaluation problem and overcome the possible occurrence of selection bias. When using non-experimental data, different evaluation approaches can be thought of. The aim of this paper is to review the most relevant estimators, discuss their identifying assumptions and their (dis-)advantages. Thereby we will present estimators based on some form of exogeneity (selection on observables) as well as estimators where selection might also occur on unobservable characteristics. Since the possible occurrence of effect heterogeneity has become a major topic in evaluation research in recent years, we will also assess the ability of each estimator to deal with it. Additionally, we will also discuss some recent extensions of the static evaluation framework to allow for dynamic treatment evaluation. The authors thank Stephan L. Thomsen, Christopher Zeiss and one anonymous referee for valuable comments. The usual disclaimer applies.     

Some new results on the cumulative residual entropy

The residual entropy function is a relevant dynamic measure of uncertainty in reliability and survival studies. Recently, Rao et al. [2004. Cumulative residual entropy: a new measure of information. IEEE Transactions on Information Theory 50, 1220–1228] and Asadi and Zohrevand [2007. On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference 137, 1931–1941] define the cumulative residual entropy and the dynamic cumulative residual entropy, respectively, as some new measures of uncertainty. They study some properties and applications of these measures showing how the cumulative residual entropy and the dynamic cumulative residual entropy are connected with the mean residual life function. In this paper, we obtain some new results on these functions. We also define and study the dynamic cumulative past entropy function. Some results are given connecting these measures of a lifetime distribution and that of the associated weighted distribution.     

Efficient semiparametric estimation in generalized partially linear additive models

In this paper we study semiparametric generalized additive models in which some part of the additive function is linear. We study the semiparametric efficiency under this regression model for the exponential family. We also present an asymptotically efficient estimation procedure based on the generalized profile likelihood approach.     

基于GMM的教育投资与经济增长分析

教育投资对经济增长具有促进作用已得到公认。以我国各个省市区作为横截面单元．利用各个横截面单元1998—2007年的样本组成的面板数据,建立动态面板数据模型采用广义矩估计方法来分析教育投资对经济增长的动态效应,发现教育投资对经济增长具有长期的促进作用,并且在逐年增强;分地区来看,略有差异。     

Calibration as estimation

Calibration in macroeconomics involves choosing fre parameters by matching certain moments of simulted models with those of data. We formally examine this method by treating the process of calibration as an econometric estimator. A numerical version of the Mehra-Prescott (1985) economy is the setting for an evaluation of calibration estimators via Monte Carlo methods. While these estimators sometimes have reasonable finite-sample properties they are not robust to mistakes in setting non-free parameters. In contrast, generalized method-of-moments (GMM) estimators have satisfactory finite-sample characteristics, quick convergence, and informational requirements less stringent than those of calibration estimators. In dynamic equilibrium models in which GMM is infeasible we offer some suggestions for improving estimates based on calibration methodology.     

Multidimensional Poverty: Measurement,Estimation, and Inference

Calibration in macroeconomics involves choosing fre parameters by matching certain moments of simulted models with those of data. We formally examine this method by treating the process of calibration as an econometric estimator. A numerical version of the Mehra-Prescott (1985) economy is the setting for an evaluation of calibration estimators via Monte Carlo methods. While these estimators sometimes have reasonable finite-sample properties they are not robust to mistakes in setting non-free parameters. In contrast, generalized method-of-moments (GMM) estimators have satisfactory finite-sample characteristics, quick convergence, and informational requirements less stringent than those of calibration estimators. In dynamic equilibrium models in which GMM is infeasible we offer some suggestions for improving estimates based on calibration methodology.     

Bivariate extension of generalized cumulative past entropy

The cumulative past entropy (CPE) of order α, a dual measure of cumulative residual entropy (CRE) of order α, has recently been proposed as a suitable extension of CPE. In this article, we extend the definition of (dynamic) CPE of order α (DCPE(α)) to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE(α) for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE(α) are obtained for conditional distributions. Along with some characterization results it is shown that the proposed generalized measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure and prove interrelation with some existing stochastic orders.     

A quantile-based generalized dynamic cumulative measure of entropy

The cumulative residual entropy (CRE), introduced by Rao et al. (2004), is a new measure of uncertainty and viewed as a dynamic measure of uncertainty. Asadi and Zohrevand (2007) proposed a dynamic form of the CRE, namely dynamic CRE. Recently, Kumar and Taneja (2011) introduced a generalized dynamic CRE based on the Varma entropy introduced by Varma (1966) and called it dynamic CRE of order α and type β. In the present article, we introduce a quantile version of the dynamic CRE of order α and type β and study its properties. For this measure, we obtain some characterization results, aging classes properties, and stochastic comparisons.     

Weighted extensions of generalized cumulative residual entropy and their applications

Abstract

In this paper, we consider weighted extensions of generalized cumulative residual entropy and its dynamic(residual) version. Our results include linear transformations, stochastic ordering, bounds, aging class properties and some relationships with other reliability concepts. We also define the conditional weighted generalized cumulative residual entropy and discuss some properties of its. For these concepts, we obtain some characterization results under some assumptions. Finally, we provide an estimator of the new information measure using empirical approach. In addition, we study large sample properties of this estimator.     

Transform orders and stochastic monotonicity of statistical functionals

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such a behavior in terms of the usual stochastic order. For this purpose, we introduce a generalized family of stochastic orders, which is referred to as transform orders, showing that it provides a flexible framework for deriving stochastic monotonicity results. Given that our general definition makes it possible to obtain some well known ordering relations as particular cases, we can easily apply our method to different families of functionals. These include some prominent inequality measures, such as the generalized entropy, the Gini index, and its generalizations. We also illustrate the applicability of our approach by determining the least favorable distribution, and the behavior of some bootstrap statistics, in some goodness-of-fit testing procedures.     

On diagnostic devices for proposing half-logistic and inverse half-logistic models using generalized (k) record values

In this work we consider the generalized upper (k) record values (GURV’s) and generalized lower (k) record values (GLRV’s) arising from half-logistic distribution (HLD) and inverse half-logistic distribution (IHLD). We derive some characterization results of HLD based on some moment relations of generalized upper (k) record values and those of generalized lower (k) record values and accordingly devised some diagnostic tools to identify HLD as a model to the distribution of a population. Similar characterization theorems and diagnostic tools are developed for IHLD as well. Simulation studies are conducted to validate the diagnostic tools devised for both HLD and IHLD.     

Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

The use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.     

On Multi-Treatment Adaptive Allocation Design for Dichotomous Response

The use of ridit, as a probability score, is a very common practice to compare discrete random variables in discrete data analysis. In the present work we formulate ridit reliability functionals for some comparison of K independent binary random variables. We use such functionals to provide a generalized response-adaptive design (GRAD) on K(≥ +2) treatment-arms for dichotomous response variables. We exhibit some properties of the proposed design and compare it with some of the existing competitors by computing its various performance measures. We also provide a discussion towards a possible modification of the GRAD in the presence of covariates.     

Tail-Adaptive Location Rank Test for the Generalized Secant Hyperbolic Distribution

The generalized secant hyperbolic distribution (GSHD) was recently introduced as a modeling tool in data analysis. The GSHD is a unimodal distribution that is completely specified by location, scale, and shape parameters. It has also been shown elsewhere that the rank procedures of location are regular, robust, and asymptotically fully efficient. In this article, we study certain tail weight measures for the GSHD and introduce a tail-adaptive rank procedure of location based on those tail weight measures. We investigate the properties of the new adaptive rank procedure and compare it to some conventional estimators.     

A dynamic double asymmetric copula generalized autoregressive conditional heteroskedasticity model: application to China's and US stock market

Modeling the relationship between multiple financial markets has had a great deal of attention in both literature and real-life applications. One state-of-the-art technique is that the individual financial market is modeled by generalized autoregressive conditional heteroskedasticity (GARCH) process, while market dependence is modeled by copula, e.g. dynamic asymmetric copula-GARCH. As an extension, we propose a dynamic double asymmetric copula (DDAC)-GARCH model to allow for the joint asymmetry caused by the negative shocks as well as by the copula model. Furthermore, our model adopts a more intuitive way of constructing the sample correlation matrix. Our new model yet satisfies the positive-definite condition as found in dynamic conditional correlation-GARCH and constant conditional correlation-GARCH models. The simulation study shows the performance of the maximum likelihood estimate for DDAC-GARCH model. As a case study, we apply this model to examine the dependence between China and US stock markets since 1990s. We conduct a series of likelihood ratio test tests that demonstrate our extension (dynamic double joint asymmetry) is adequate in dynamic dependence modeling. Also, we propose a simulation method involving the DDAC-GARCH model to estimate value at risk (VaR) of a portfolio. Our study shows that the proposed method depicts VaR much better than well-established variance–covariance method.     

ERROR BOUNDS FOR CALCULATION OF THE GITTINS INDICES

For a wide class of semi-Markov decision processes the optimal policies are expressible in terms of the Gittins indices, which have been found useful in sequential clinical trials and pharmaceutical research planning. In general, the indices can be approximated via calibration based on dynamic programming of finite horizon. This paper provides some results on the accuracy of such approximations, and, in particular, gives the error bounds for some well known processes (Bernoulli reward processes, normal reward processes and exponential target processes).