Generalized Kerridge’s inaccuracy measure for conditionally specified models

Recently, conditional Renyi’s divergence of order α and Kerridge’s inaccuracy measures are studied by Navarro et al. (2014 Navarro, J., Sunoj, S.M., Linu, M.N. (2014). Characterizations of bivariate models using some dynamic conditional information divergence measures. Commun. Stat. Theory Methods 43:1939–1948.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). In the present article, a generalized dynamic conditional Kerridge’s inaccuracy measure is introduced, which can be represented as the sum of conditional Renyi’s divergence and Renyi’s entropy. Some useful bounds are obtained using the concept of likelihood ratio order. The results are extended to weighted distributions. Sufficient conditions are obtained for the monotonicity of the proposed measure. Characterizations for bivariate exponential conditional distribution are presented based on the proposed measure.     

Improved estimation methods for unrelated question randomized response techniques

The randomized response technique (RRT) is an important tool, commonly used to avoid biased answers in survey on sensitive issues by preserving the respondents’ privacy. In this paper, we introduce a data collection method for survey on sensitive issues combining both the unrelated-question RRT and the direct question design. The direct questioning method is utilized to obtain responses to a non sensitive question that is related to the innocuous question from the unrelated-question RRT. These responses serve as additional information that can be used to improve the estimation of the prevalence of the sensitive behavior. Furthermore, we propose two new methods for the estimation of the proportion of respondents possessing the sensitive attribute under a missing data setup. More specifically, we develop the weighted estimator and the weighted conditional likelihood estimator. The performances of our estimators are studied numerically and compared with that of an existing one. Both proposed estimators are more efficient than the Greenberg's estimator. We illustrate our methods using real data from a survey study on illegal use of cable TV service in Taiwan.     

Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes

In this article, we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted integrated conditional moment (ICM) test of Bierens (1984 Bierens, H. J. (1984). Model specification testing of time series regressions. Journal of Econometrics 26:323–353.[Crossref], [Web of Science ®] , [Google Scholar]) for time series regression models with the simulated ICM test of Bierens and Wang (2012 Bierens, H. J., Wang, L. (2012). Integrated conditional moment tests for parametric conditional distributions. Econometric Theory 28:328–362.[Crossref], [Web of Science ®] , [Google Scholar]) of conditional distribution models for cross-section data. To the best of our knowledge, no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors.     

均值—条件风险价值模型有效前沿分析——以含无风险资产和持有期为研究视角

从有效投资组合的角度构建持有期下含有无风险资产的均值—条件风险价值模型,用Lagrange乘子法对该模型求解,可得到:一定条件下,新模型的有效前沿与均值—方差模型有效前沿是一致的;且当借贷利率不同时,新模型的有效前沿可以根据组合预期收益率与借贷利率的不同关系,由线段、双曲线以及射线三个部分组合而成。     

On gart's test for interaction of second order

Gart (1972) ottered a Statistic on testing the hypothesis of no second-order interaction in a 2×s×t contingency table. The statistic was tn be used as an asymptotic chi-square with (s-1) (t-1) degrees of freedom. We show that this statistic suiters from the drawback that unless certain side conditions hold, the statistic would reject the null hypothesis with probability approaching one asymptotically even in the null case. Hence the statistic is not strictly valid for the hypothesis for which it was intended.     

Measurement Error Correction by Exploiting Gene–Environment Independence in Family‐Based Case–Control Studies

Abstract. Family‐based case–control designs are commonly used in epidemiological studies for evaluating the role of genetic susceptibility and environmental exposure to risk factors in the etiology of rare diseases. Within this framework, it is often reasonable to assume genetic susceptibility and environmental exposure being conditionally independent of each other within families in the source population. We focus on this setting to explore the situation of measurement error affecting the assessment of the environmental exposure. We correct for measurement error through a likelihood‐based method. We exploit a conditional likelihood approach to relate the probability of disease to the genetic and the environmental risk factors. We show that this approach provides less biased and more efficient results than that based on logistic regression. Regression calibration, instead, provides severely biased estimators of the parameters. The comparison of the correction methods is performed through simulation, under common measurement error structures.     

Bayesian inference of asymmetric stochastic conditional duration models

This paper extends stochastic conditional duration (SCD) models for financial transaction data to allow for correlation between error processes and innovations of observed duration process and latent log duration process. Suitable algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting SCD models under various distributional assumptions about the innovation of the measurement equation. Unlike the estimation methods commonly used to estimate the SCD models in the literature, we work with the original specification of the model, without subjecting the observation equation to a logarithmic transformation. Results of simulation studies suggest that our proposed models and corresponding estimation methodology perform quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts of the fitted models. Applications to the IBM transaction data allow comparison of our models and methods to those existing in the literature.     

Distribution theory and inference for polynomial-normal densities

This paper considers a class of densities formed by taking the product of nonnegative polynomials and normal densities. These densities provide a rich class of distributions that can be used in modelling when faced with non-normal characteristics such as skewness and multimodality. In this paper we address inferential and computational issues arising in the practical implementation of this parametric family in the context of the linear model. Exact results are recorded for the conditional analysis of location-scale models and an importance sampling algorithm is developed for the implementation of a conditional analysis for the general linear model when using polynomial-normal distributions for the error.     

Multiple deletion measures and conditional influence in regression model

The joint effect of the deletion of the ith and jih cases is given by Gray and Ling (1984), they discussed the influence measures for influential subsets in linear regression analysis. The present paper is concerned with multiple sets of deletion measures in the linear regression model. In particular we are interested in the effects of the jointly and conditional influence analysis for the detection of two influential subsets.     

ROC Curves in Non‐Parametric Location‐Scale Regression Models

Abstract. The receiver operating characteristic (ROC) curve is a tool of extensive use to analyse the discrimination capability of a diagnostic variable in medical studies. In certain situations, the presence of a covariate related to the diagnostic variable can increase the discriminating power of the ROC curve. In this article, we model the effect of the covariate over the diagnostic variable by means of non‐parametric location‐scale regression models. We propose a new non‐parametric estimator of the conditional ROC curve and study its asymptotic properties. We also present some simulations and an illustration to a data set concerning diagnosis of diabetes.