Marginal Nested Interactions for Contingency Tables

We introduce a new definition of generalized marginal interactions, called marginal nested interactions, which includes baseline, local, continuation and reverse continuation logits and odds ratios as special cases. The significant aspect of this definition is the inclusion of new types of logits and odds ratios that can handle non-ordinal, ordinal and partially ordered categorical variables in a flexible and appropriate way. It is proved also that the marginal nested interactions define a saturated model of a multi-way contingency table.     

The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes

Abstract.  The Pearson diffusions form a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein–Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. Explicit optimal martingale estimating functions are found. The discussion covers GMM, quasi-likelihood, non-linear weighted least squares estimation and likelihood inference too. The analytical tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions and Pearson stochastic volatility models. For the non-Markov models, explicit optimal prediction-based estimating functions are found. The estimators are shown to be consistent and asymptotically normal.     

广东农村居民消费行为研究

本文根据凯恩斯消费理论,建立广东省农村居民消费性支出Ct关于农村居民人均纯收入Yt的回归模型,并通过利用农村居民消费价格指数这一指标,消除价格变动对实际货币购买力的影响。接着引入两个虚拟变量,考虑利息税和农村税费改革对居民消费的影响,并且对其进行经济意义的解释,深刻分析广东农村居民消费行为变化的原因。然后通过时间序列分析,预测出2008年和2009年的实际消费性支出,为相关的经济决策提供依据,并根据以上的分析结果给出了关于促进广东农村居民消费的建议。     

On asymptotic properties of Bayesian partially linear models

In this paper, we present large sample properties of a partially linear model from the Bayesian perspective, in which responses are explained by the semiparametric regression model with the additive form of the linear component and the nonparametric component. For this purpose, we investigate asymptotic behaviors of posterior distributions in terms of consistency. Specifically, we deal with a specific Bayesian partially linear regression model with additive noises in which the nonparametric component is modeled using Gaussian process priors. Under the Bayesian partially linear model using Gaussian process priors, we focus on consistency of posterior distribution and consistency of the Bayes factor, and extend these results to generalized additive regression models and study their asymptotic properties. In addition we illustrate the asymptotic properties based on empirical analysis through simulation studies.     

General partially linear varying-coefficient transformation model with right censored data

In this paper, a unified maximum marginal likelihood estimation procedure is proposed for the analysis of right censored data using general partially linear varying-coefficient transformation models (GPLVCTM), which are flexible enough to include many survival models as its special cases. Unknown functional coefficients in the models are approximated by cubic B-spline polynomial. We estimate B-spline coefficients and regression parameters by maximizing marginal likelihood function. One advantage of this procedure is that it is free of both baseline and censoring distribution. Through simulation studies and a real data application (VA data from the Veteran's Administration Lung Cancer Study Clinical Trial), we illustrate that the proposed estimation procedure is accurate, stable and practical.     

A method for modifying multiple testing procedures

Many recent multiple testing papers have provided more efficient and/or robust methodology for control of a particular error rate. However, different multiple testing scenarios call for the control of different error rates. Hence, the procedure possessing the desired optimality and/or robustness properties may not be applicable to the problem at hand. This paper provides a general method for extending any multiple testing procedure to control any error rate, thereby allowing for the procedure possessing the desired properties to be used to control the most relevant error rate. As an example, two popular procedures that were originally designed to control the marginal and positive False Discovery Rate are extended to control the False Discovery Rate and Family-wise Error Rate. It is shown that optimality and/or robustness properties of the original procedure are retained when it is modified using the proposed method.     

Orthogonal decomposition of point-symmetry for multiway tables

For multiway contingency tables, Wall and Lienert (Biom. J. 18:259–264, 1976) considered the point-symmetry model. For square contingency tables, Tomizawa (Biom. J. 27:895–905, 1985) gave a theorem that the point-symmetry model holds if and only if both the quasi point-symmetry and the marginal point-symmetry models hold. This paper proposes some quasi point-symmetry models and marginal point-symmetry models for multiway tables, and extends Tomizawa’s (Biom. J. 27:895–905, 1985) theorem into multiway tables. We also show that for multiway tables the likelihood ratio statistic for testing goodness of fit of the point-symmetry model is asymptotically equivalent to the sum of those for testing the quasi point-symmetry model with some order and the marginal point-symmetry model with the corresponding order. An example is given.     

Decision support for lead time and demand variability reduction

Companies undertaking operations improvement in supply chains face many alternatives. This work seeks to assist practitioners to prioritize improvement actions by developing analytical expressions for the marginal values of three parameters – (i) lead time mean, (ii) lead time variance, and (iii) demand variance – which measure the marginal cost of an incremental change in a parameter. The relative effectiveness of reducing lead time mean versus lead time variance is captured by the ratio of the marginal value of lead time mean to that of lead time variance. We find that this ratio strongly depends on whether the lead time mean and variance are independent or correlated. We illustrate the application of the results with a numerical example from an industrial setting. The insights can help managers determine the optimal investment decision to modify demand and supply characteristics in their supply chain, e.g., by switching suppliers, factory layout, or investing in information systems.     

Tests for homogeneity of extreme value scale parameters

It is often assumed in situations in which life data from Weibull or extreme-value distributions are involved that data in different samples come from extreme-value distributions with the same scale parameter (equivalently, Weibull distributions with the same shape parameter). This paper proposes a number of tests for homogeneity for extreme-value scale parameters, based on a number of commonly used estimators for these scale parameters. Previous theoretical work and some simulation results provided here indicate that the null distributions of the test statistics proposed are well approximated by the x2 distribution under a wide range of conditions