Estimating function method for product autoregressive models

The first-order product autoregressive (PAR(1)) model introduced by McKenzie in 1982 McKenzie, E. D. (1982). Product autoregression: A time series characterization of the gamma distribution. Journal of Applied Probability 19:463–468. [Google Scholar] did not attract the attention of practitioners due to the unavailability of a proper estimation method. This article proposes an estimating function (EF) method to fill the gap. In particular, we suggest an optimal combination of linear and quadratic EFs to overcome the problem of parameter identification. The procedure is applied to Weibull and Gamma PAR(1) models. Simulation and data analysis show that the proposed method performs better than the existing methods.     

一种新的金融动态横截面估计方法——基于中国股票市场条件定价模型评估的应用与扩展

大多数资产定价模型常常用静态横截面回归(the static cross-sectional regression)进行定价表现评估,从而投资组合回报率的时间变化性并不能被时变的风险承载或者(和)时变的风险溢价所解释.本文从经济学的角度,运用一种新的金融动态横截面回归(the dynamic cross-sectional regression),首次考察了基于中国股票市场和美国股票市场的条件资产定价模型的定价表现:股票市场投资组合回报率的时变性是否能被时变的风险溢价所解释.本文发现,短期收益反转和流通市值加权市场换手率为条件变量的条件资本资产定价模型和基于消费的条件资本资产定价模型,能更好的解释中国股票投资组合的回报时变性,其时变性主要来自于时变的风险溢价.另外,本文发现一些拥有持续(persistence)和缓慢变化(slow-moving)特性的条件变量更能够解释横截面投资组合的时变回报.     

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.     

Optimality Of Some Two-Stage Sampling Methods

Two-stage sampling plans in which the estimator is computed from the second sample only, and has a guaranteed precision irrespective of the parameter value, are considered. We prove the following optimality property for existing strategies in binomial and Poisson populations: there exists no other

strategy, of the same form, that guarantees the same precision, without increasing the expected sample size for some parameter valucs. The method of proof is illustrnted by proving a similar result for normal populations     

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.