Inconsistency of Classical Penalized Likelihood Approaches under Endogeneity

With the high speed development of information technology, contemporary data from a variety of fields becomes extremely large. The number of features in many datasets is well above the sample size and is called high dimensional data. In statistics, variable selection approaches are required to extract the efficacious information from high dimensional data. The most popular approach is to add a penalty function coupled with a tuning parameter to the log likelihood function, which is called penalized likelihood method. However, almost all of penalized likelihood approaches only consider noise accumulation and supurious correlation whereas ignoring the endogeneity which also appeared frequently in high dimensional space. In this paper, we explore the cause of endogeneity and its influence on penalized likelihood approaches. Simulations based on five classical pe-nalized approaches are provided to vindicate their inconsistency under endogeneity. The results show that the positive selection rate of all five approaches increased gradually but the false selection rate does not consistently decrease when endogenous variables exist, that is, they do not satisfy the selection consistency.

Partial Penalized Empirical Likelihood Ratio Test Under Sparse Case

A consistent test via the partial penalized empirical likelihood approach for the parametric hy- pothesis testing under the sparse case, called the partial penalized empirical likelihood ratio （PPELR） test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypoth- esis and the local alternatives of order n-1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical like- lihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.

Dealing with detection error in site occupancy surveys: what can we do with a single survey?

Aim Site occupancy probabilities of target species are commonly used in various ecological studies,e.g.to monitor current status and trends in biodiversity.Detection error introduces bias in the estimators of site occupancy.Existing methods for estimating occupancy probability in the presence of detection error use replicate surveys.These methods assume population closure,i.e.the site occupancy status remains constant across surveys,and independence between surveys.We present an approach for estimating site occupancy probability in the presence of detection error that requires only a single survey and does not require assumption of population closure or independence.In place of the closure assumption,this method requires covariates that affect detection and occupancy.Methods Penalized maximum-likelihood method was used to estimate the parameters.Estimability of the parameters was checked using data cloning.Parametric boostrapping method was used for computing confidence intervals.Important Findings The single-survey approach facilitates analysis of historical datasets where replicate surveys are unavailable,situations where replicate surveys are expensive to conduct and when the assumptions of closure or independence are not met.This method saves significant amounts of time,energy and money in ecological surveys without sacrificing statistical validity.Further,we show that occupancy and habitat suitability are not synonymous and suggest a method to estimate habitat suitability using single-survey data.

A two-step method for estimating high-dimensional Gaussian graphical models

The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likelihood-based. In this paper, we propose a two-step method for estimating the high-dimensional Gaussian graphical model. Specifically, the first step serves as a screening step, in which many entries of the concentration matrix are identified as zeros and thus removed from further consideration. Then in the second step, we focus on the remaining entries of the concentration matrix and perform selection and estimation for nonzero entries of the concentration matrix. Since the dimension of the parameter space is effectively reduced by the screening step,the estimation accuracy of the estimated concentration matrix can be potentially improved. We show that the proposed method enjoys desirable asymptotic properties. Numerical comparisons of the proposed method with several existing methods indicate that the proposed method works well. We also apply the proposed method to a breast cancer microarray data set and obtain some biologically meaningful results.

Local Influence Analysis for Semiparametric Reproductive Dispersion Nonlinear Models

The present paper proposes a semiparametric reproductive dispersion nonlinear model （SRDNM） which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates （MPLEs） of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.

SICA for Cox's Proportional Hazards Model with a Diverging Number of Parameters

The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.

Order shrinkage and selection for the INGARCH(p,q)model

The integer-valued generalized autoregressive conditional heteroskedastic(INGARCH)model is often utilized to describe data in biostatistics,such as the number of people infected with dengue fever,daily epileptic seizure counts of an epileptic patient and the number of cases of campylobacterosis infections,etc.Since the structure of such data is generally high-order and sparse,studies about order shrinkage and selection for the model attract many attentions.In this paper,we propose a penalized conditional maximum likelihood(PCML)method to solve this problem.The PCML method can effectively select significant orders and estimate the parameters,simultaneously.Some simulations and a real data analysis are carried out to illustrate the usefulness of our method.