Quantile regression and variable selection for the single-index model

In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set.     

Oracle GMM estimation for misspecified models via thresholding

We propose a thresholding generalized method of moments (GMM) estimator for misspecified time series moment condition models. This estimator has the following oracle property: its asymptotic behavior is the same as of any efficient GMM estimator obtained under the a priori information that the true model were known. We propose data adaptive selection methods for thresholding parameter using multiple testing procedures. We determine the limiting null distributions of classical parameter tests and show the consistency of the corresponding block-bootstrap tests used in conjunction with thresholding GMM inference. We present the results of a simulation study for a misspecified instrumental variable regression model and for a vector autoregressive model with measurement error. We illustrate an application of the proposed methodology to data analysis of a real-world dataset.     

Simultaneous structure estimation and variable selection in partial linear varying coefficient models for longitudinal data

Partial linear varying coefficient models (PLVCM) are often considered for analysing longitudinal data for a good balance between flexibility and parsimony. The existing estimation and variable selection methods for this model are mainly built upon which subset of variables have linear or varying effect on the response is known in advance, or say, model structure is determined. However, in application, this is unreasonable. In this work, we propose a simultaneous structure estimation and variable selection method, which can do simultaneous coefficient estimation and three types of selections: varying and constant effects selection, relevant variable selection. It can be easily implemented in one step by employing a penalized M-type regression, which uses a general loss function to treat mean, median, quantile and robust mean regressions in a unified framework. Consistency in the three types of selections and oracle property in estimation are established as well. Simulation studies and real data analysis also confirm our method.     

On a Class of Nonlinear AR(P) Models with Nonlinear ARCH Errors

This paper studies general sufficient conditions for the geometric ergodicity and the existence of moments for a class of nonlinear autoregressive models with nonlinear ARCH errors. Applications of these conditions to various well-known nonlinear time series models yield specific sufficient conditions, many of which are new or generalizations of existing conditions.     

A variable selection approach to monotonic regression with Bernstein polynomials

One of the standard problems in statistics consists of determining the relationship between a response variable and a single predictor variable through a regression function. Background scientific knowledge is often available that suggests that the regression function should have a certain shape (e.g. monotonically increasing or concave) but not necessarily a specific parametric form. Bernstein polynomials have been used to impose certain shape restrictions on regression functions. The Bernstein polynomials are known to provide a smooth estimate over equidistant knots. Bernstein polynomials are used in this paper due to their ease of implementation, continuous differentiability, and theoretical properties. In this work, we demonstrate a connection between the monotonic regression problem and the variable selection problem in the linear model. We develop a Bayesian procedure for fitting the monotonic regression model by adapting currently available variable selection procedures. We demonstrate the effectiveness of our method through simulations and the analysis of real data.     

论我国开征物业税对不同利益主体的影响

为建立和健全我国财产税体系,规范税费制度,降低建筑业及房地产业的经营成本,开征物业税已是大势所趋。围绕开征物业税对政府、房产商及房产市场、居民等不同群体利益的影响,进行了由上而下的立体性分析。     

股票市场状态的动力学过程分析

就股票市场呈现的变化归纳为四种状态,即随机游走态、扩散漂移态、混沌震荡态、连贯平稳态,并对每一状态给出了动力学过程的数学描述,研究了各种"过程"下方程的解,以及各种状态下对股市价格带来的系统效应.从股市的微观结构出发,探讨了四种状态下的股市特征表现及投资者的操作策略,为实时地预测股市发展提供了辅助决策.