Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength

In this paper, we estimate multicomponent stress-strength reliability by assuming Burr-XII distribution. The research methodology adopted here is to estimate the parameter using maximum likelihood estimation. Reliability is estimated using the maximum likelihood method of estimation and results are compared using the Monte Carlo simulation for small samples. Using real data sets we illustrate the procedure clearly.     

Extended BIC for linear regression models with diverging number of relevant features and high or ultra-high feature spaces

In many conventional scientific investigations with high or ultra-high dimensional feature spaces, the relevant features, though sparse, are large in number compared with classical statistical problems, and the magnitude of their effects tapers off. It is reasonable to model the number of relevant features as a diverging sequence when sample size increases. In this paper, we investigate the properties of the extended Bayes information criterion (EBIC) (Chen and Chen, 2008) for feature selection in linear regression models with diverging number of relevant features in high or ultra-high dimensional feature spaces. The selection consistency of the EBIC in this situation is established. The application of EBIC to feature selection is considered in a SCAD cum EBIC procedure. Simulation studies are conducted to demonstrate the performance of the SCAD cum EBIC procedure in finite sample cases.     

Sieve Estimation of Time-Varying Panel Data Models With Latent Structures

We propose a heterogeneous time-varying panel data model with a latent group structure that allows the coefficients to vary over both individuals and time. We assume that the coefficients change smoothly over time and form different unobserved groups. When treated as smooth functions of time, the individual functional coefficients are heterogeneous across groups but homogeneous within a group. We propose a penalized-sieve-estimation-based classifier-Lasso (C-Lasso) procedure to identify the individuals’ membership and to estimate the group-specific functional coefficients in a single step. The classification exhibits the desirable property of uniform consistency. The C-Lasso estimators and their post-Lasso versions achieve the oracle property so that the group-specific functional coefficients can be estimated as well as if the individuals’ membership were known. Several extensions are discussed. Simulations demonstrate excellent finite sample performance of the approach in both classification and estimation. We apply our method to study the heterogeneous trending behavior of GDP per capita across 91 countries for the period 1960–2012 and find four latent groups.     

Penalized Maximum Likelihood Principle for Choosing Ridge Parameter

We consider the problem of choosing the ridge parameter. Two penalized maximum likelihood (PML) criteria based on a distribution-free and a data-dependent penalty function are proposed. These PML criteria can be considered as “continuous” versions of AIC. A systematic simulation is conducted to compare the suggested criteria to several existing methods. The simulation results strongly support the use of our method. The method is also applied to two real data sets.     

Tuning Parameter Estimation in Penalized Least Squares Methodology

The efficiency of the penalized methods (Fan and Li, 2001 Fan , J. , Li , R. ( 2001 ). Variable selection via nonconcave penalized likelihood and its oracle properties . Journal of the American Statistical Association 96 : 1348 – 1360 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) depends strongly on a tuning parameter due to the fact that it controls the extent of penalization. Therefore, it is important to select it appropriately. In general, tuning parameters are chosen by data-driven approaches, such as the commonly used generalized cross validation. In this article, we propose an alternative method for the derivation of the tuning parameter selector in penalized least squares framework, which can lead to an ameliorated estimate. Simulation studies are presented to support theoretical findings and a comparison of the Type I and Type II error rates, considering the L ₁, the hard thresholding and the Smoothly Clipped Absolute Deviation penalty functions, is performed. The results are given in tables and discussion follows.     

Function-on-function regression for two-dimensional functional data

ABSTRACT

We present methods for modeling and estimation of a concurrent functional regression when the predictors and responses are two-dimensional functional datasets. The implementations use spline basis functions and model fitting is based on smoothing penalties and mixed model estimation. The proposed methods are implemented in available statistical software, allow the construction of confidence intervals for the bivariate model parameters, and can be applied to completely or sparsely sampled responses. Methods are tested to data in simulations and they show favorable results in practice. The usefulness of the methods is illustrated in an application to environmental data.     

Variable Selection in Joint Location and Scale Models of the Skew-t-Normal Distribution

Variable selection is an important issue in all regression analysis, and in this article, we investigate the simultaneous variable selection in joint location and scale models of the skew-t-normal distribution when the dataset under consideration involves heavy tail and asymmetric outcomes. We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. These estimators are compared by simulation studies.     

Comparison of Ordinary and Penalized Power-Divergence Test Statistics for Small and Moderate Samples in Three-Way Contingency Tables via Simulation

In this article, size and power properties of the ordinary and penalized power-divergence test statistics have been compared to test a nested sequence of log-linear models for various penalization and λ values. 2 × 2 × 2 contingency tables distributed according to a multinomial distribution are considered. The simulation study results reveal that the penalized power-divergence test statistics with penalization value of one and λ = ?1.5, ?2 are the best choices for small and moderate samples, respectively.     

Bridge regression: Adaptivity and group selection

In high-dimensional regression problems regularization methods have been a popular choice to address variable selection and multicollinearity. In this paper we study bridge regression that adaptively selects the penalty order from data and produces flexible solutions in various settings. We implement bridge regression based on the local linear and quadratic approximations to circumvent the nonconvex optimization problem. Our numerical study shows that the proposed bridge estimators are a robust choice in various circumstances compared to other penalized regression methods such as the ridge, lasso, and elastic net. In addition, we propose group bridge estimators that select grouped variables and study their asymptotic properties when the number of covariates increases along with the sample size. These estimators are also applied to varying-coefficient models. Numerical examples show superior performances of the proposed group bridge estimators in comparisons with other existing methods.     

基于ML指数法的中国银行业贷款效率分析

阐述ML(Malmquist-Luenberger)指数构成及其分解方法,使用2007—2012年银行业相关数据计算考虑不良贷款的前提下投入产出导向的银行业贷款ML指数及其分解,结果表明在6年考察期间我国银行业贷款效率平均有0.002的降低,其原因是技术进步指数及规模效率指数降低。这说明银行贷款技术在大范围地普及,而贷款技术创新及贷款规模有待进一步发展,在市场发展中应密切关注经济萎缩的可能,并据此提出提高银行业贷款效率的建议。