Mixtures of regression models with incomplete and noisy data

The estimation of the mixtures of regression models is usually based on the normal assumption of components and maximum likelihood estimation of the normal components is sensitive to noise, outliers, or high-leverage points. Missing values are inevitable in many situations and parameter estimates could be biased if the missing values are not handled properly. In this article, we propose the mixtures of regression models for contaminated incomplete heterogeneous data. The proposed models provide robust estimates of regression coefficients varying across latent subgroups even under the presence of missing values. The methodology is illustrated through simulation studies and a real data analysis.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

A robust test for autocorrelation in the presence of a structural break in variance

It has been known that when there is a break in the variance (unconditional heteroskedasticity) of the error term in linear regression models, a routine application of the Lagrange multiplier (LM) test for autocorrelation can cause potentially significant size distortions. We propose a new test for autocorrelation that is robust in the presence of a break in variance. The proposed test is a modified LM test based on a generalized least squares regression. Monte Carlo simulations show that the new test performs well in finite samples and it is especially comparable to other existing heteroskedasticity-robust tests in terms of size, and much better in terms of power.     

Optimal quantization applied to sliced inverse regression

In this paper we consider a semiparametric regression model involving a d-dimensional quantitative explanatory variable X and including a dimension reduction of X via an index β′X. In this model, the main goal is to estimate the Euclidean parameter β and to predict the real response variable Y conditionally to X. Our approach is based on sliced inverse regression (SIR) method and optimal quantization in L^p-norm. We obtain the convergence of the proposed estimators of β and of the conditional distribution. Simulation studies show the good numerical behavior of the proposed estimators for finite sample size.     

An m-estimation-based model selection criterion with a data-oriented penalty

In Wu and Zen (1999), a linear model selection procedure based on M-estimation is proposed, which includes many classical model selection criteria as its special cases, and it is shown that the selection procedure is strongly consistent for a variety of penalty functions. In this paper, we will investigate its small sample performances for some choices of fixed penalty functions. It can be seen that the performance varies with the choice of the penalty. Hence, a randomized penalty based on observed data is proposed, which preserves the consistency property and provides improved performance over a fixed choice of penalty functions.     

陕西省人口城市化Logistic模型及其应用——基于结构突变的理论分析

城市化是走向现代化的必经阶段,准确的城市化预测是进行经济、社会建设的基础。在结构突变理论的基础上,用Logistic模型对1978～2010年陕西城市化率进行分析。结论表明：1999年为陕西城市化率的结构突变点,说明城市化率的增长受到外部冲击的影响,分段以后的拟合优度明显提高。分别以阈值0.8和1进行分阶段构建的Logistic拟合精度明显提高,但阈值为1的精度更高,说明陕西城市化还在加速,预测表明到2030年陕西城市化率将达到70%左右。总体而言,从1984年到2030年为陕西省城市化的加速阶段。城市化加速阶段的住房问题、人口膨胀、环境恶化、交通拥挤、社会治安问题必须妥善解决。     

BUSDM – an algorithm for the bottom-up search of departures from a model

Searching for regions of the input space where a statistical model is inappropriate is useful in many applications. The study proposes an algorithm for finding local departures from a regression-type prediction model. The algorithm returns low-dimensional hypercubes where the average prediction error clearly departs from zero. The study describes the developed algorithm, and shows successful applications on the simulated and real data from the steel plate production. The algorithms that have been originally developed for searching regions of the high-response value from the input space are reviewed and considered as alternative methods for locating model departures. The proposed algorithm succeeds in locating the model departure regions better than the compared alternatives. The algorithm can be utilized in sequential follow-up of a model as time goes along and new data are observed.     

Interval-valued data regression using partial linear model

Semi-parametric modelling of interval-valued data is of great practical importance, as exampled by applications in economic and financial data analysis. We propose a flexible semi-parametric modelling of interval-valued data by integrating the partial linear regression model based on the Center & Range method, and investigate its estimation procedure. Furthermore, we introduce a test statistic that allows one to decide between a parametric linear model and a semi-parametric model, and approximate its null asymptotic distribution based on wild Bootstrap method to obtain the critical values. Extensive simulation studies are carried out to evaluate the performance of the proposed methodology and the new test. Moreover, several empirical data sets are analysed to document its practical applications.     

Stationary bootstrapping for realized covariations of high frequency financial data

This paper studies the stationary bootstrap applicability for realized covariations of high frequency asynchronous financial data. The stationary bootstrap method, which is characterized by a block-bootstrap with random block length, is applied to estimate the integrated covariations. The bootstrap realized covariance, bootstrap realized regression coefficient and bootstrap realized correlation coefficient are proposed, and the validity of the stationary bootstrapping for them is established both for large sample and for finite sample. Consistencies of bootstrap distributions are established, which provide us valid stationary bootstrap confidence intervals. The bootstrap confidence intervals do not require a consistent estimator of a nuisance parameter arising from nonsynchronous unequally spaced sampling while those based on a normal asymptotic theory require a consistent estimator. A Monte-Carlo comparison reveals that the proposed stationary bootstrap confidence intervals have better coverage probabilities than those based on normal approximation.     

Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits

We propose a semiparametric estimator for single‐index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non‐parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy‐tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set.