Bivariate prior distributions via branching exchangeable sequences

This paper provides a novel approach to constructing bivariate prior distributions. The idea is based on the notion of partial exchangeability. In particular, in a simple extension of the exchangeable sequence, we create two dependent exchangeable sequences via a branching mechanism. This implies the existence of a bivariate prior distribution.     

Analysis of least squares regression estimates in case of additional errors in the variables

Estimation of a regression function from independent and identical distributed data is considered. The L₂ error with integration with respect to the design measure is used as error criterion. Upper bounds on the L₂ error of least squares regression estimates are presented, which bound the error of the estimate in case that in the sample given to the estimate the values of the independent and the dependent variables are pertubated by some arbitrary procedure. The bounds are applied to analyze regression-based Monte Carlo methods for pricing American options in case of errors in modelling the price process.     

A fuzzy robust regression approach applied to bedload transport data

Fuzzy least-square regression can be very sensitive to unusual data (e.g., outliers). In this article, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to outliers. In this regard, based on the least trimmed square estimation method, an estimation procedure is proposed for determining the coefficients of the fuzzy regression model for crisp input-fuzzy output data. The investigated fuzzy regression model is applied to bedload transport data forecasting suspended load by discharge based on a real world data. The accuracy of the proposed method is compared with the well-known fuzzy least-square regression model. The comparison results reveal that the fuzzy robust regression model performs better than the other models in suspended load estimation for the particular dataset. This comparison is done based on a similarity measure between fuzzy sets. The proposed model is general and can be used for modeling natural phenomena whose available observations are reported as imprecise rather than crisp.     

中国系统性金融风险对宏观经济的影响研究

基于2007年1月至2017年12月月度数据,本文首先选取金融机构极值风险、金融体系间的传染效应、金融市场的波动性和不稳定性、流动性和信用风险4个层面的14个代表性指标测度了系统性金融风险;然后运用分位数回归度量了单个系统性风险指标对宏观经济的影响;最后运用偏最小二乘分位数回归法构建一个系统性金融风险综合指标进一步实证分析系统性金融风险对宏观经济的影响。研究结果表明：①单个系统性金融风险指数中机构极值风险类别下的指标对宏观经济的影响最大,其中金融体系巨灾风险指数影响效果最显著;②运用偏最小二乘分位数回归构造的系统性金融风险综合指标较之单个系统性金融风险指标,能够更稳健地反映系统性金融风险对宏观经济的影响状况;③从测度效果来看,单个系统性风险指标和系统性金融风险综合指标在下尾分布（0.2分位数）的结果明显优于中间分布（0.5分位数）和上尾分布（0.8分位数）。     

Asymptotic Properties of Marginal Least-Square Estimator for Ultrahigh-Dimensional Linear Regression Models with Correlated Errors

In this article, we discuss asymptotic properties of marginal least-square estimator for ultrahigh-dimensional linear regression models. We are specifically interested in probabilistic consistency of the marginal least-square estimator in the presence of correlated errors. We show that under a partial orthogonality condition, the marginal least-square estimator can achieve variable selection consistency. In addition, we demonstrate that if a mutual orthogonality holds, the marginal least-square estimator satisfies estimation consistency. The discussed theories are exemplified through extensive simulation studies.     

Bayesian quantile regression and variable selection for partial linear single-index model: Using free knot spline

Partial linear single-index model (PLSIM) has both the flexibility of nonparametric treatment and interpretability of linear term, yet existing literatures about it mainly focused on mean regression, and quantile regression analysis is scarce. Based on free knot spline approximation, we apply asymmetric Laplace distribution to implement Bayesian quantile regression, and perform variable selection in linear term and index vector via binary indicators. Our approach is exempt from regularity conditions in frequentist method, and could execute variable selection and quantile regression under mutual posterior correction, which is also the first work to implement them jointly for PLSIM in fully Bayesian framework. The numerical simulation manifests the superiority of our approach to previous methods, which embodied in better efficiency of variable selection, index vector estimates and link function approximation with different error distributions. For illustration of its application, we build a power consumption model of A₂/O process in wastewater treatment and emphatically analyze the impact of water quality factors.     

Inference in mixed proportional hazard models with <Emphasis Type="Italic">K</Emphasis> random effects

A general formulation of mixed proportional hazard models with K random effects is provided. It enables to account for a population stratified at K different levels. I then show how to approximate the partial maximum likelihood estimator using an EM algorithm. In a Monte Carlo study, the behavior of the estimator is assessed and I provide an application to the ratification of ILO conventions. Compared to other procedures, the results indicate an important decrease in computing time, as well as improved convergence and stability.     

关于语言经济原则的反思

语言经济原则是指导人类行为的一条根本性准则。经济性的语言节省了交流时间,提高了交际效率,满足了交际双方的省力需求。省力的动机不仅存在于发话人的言语生成过程中,也存在于受话人的言语理解过程中。单方面强调自身的省力欲望,不仅会降低交际效率,还可能导致交际失误,所以应注意语言经济原则的负相关性,优化配置语言资源。在实际的言语交际中,语言经济原则存在诸多不足,如省略引起交际失误,替代、指代带来交际障碍,共享知识的缺省导致交际失败。只有在语言能够充分明晰地表达意义和情感的前提下,才能使用语言经济原则。     

Robust 2k factorial design with Weibull error distributions

It is well known that the least squares method is optimal only if the error distributions are normally distributed. However, in practice, non-normal distributions are more prevalent. If the error terms have a non-normal distribution, then the efficiency of least squares estimates and tests is very low. In this paper, we consider the 2^k factorial design when the distribution of error terms are Weibull W(p,σ). From the methodology of modified likelihood, we develop robust and efficient estimators for the parameters in 2^k factorial design. F statistics based on modified maximum likelihood estimators (MMLE) for testing the main effects and interaction are defined. They are shown to have high powers and better robustness properties as compared to the normal theory solutions. A real data set is analysed.