Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood function. We derive the quadratic inference function-based estimators for the linear coefficients and the nonparametric functions when the dimension of covariates diverges, and establish asymptotic normality for the linear coefficient estimators and the rates of convergence for the nonparametric functions estimators for both finite and high-dimensional cases. The proposed method and theoretical development are quite challenging since the numbers of linear covariates and nonlinear components both increase as the sample size increases. We also propose a doubly penalized procedure for variable selection which can simultaneously identify nonzero linear and nonparametric components, and which has an asymptotic oracle property. Extensive Monte Carlo studies have been conducted and show that the proposed procedure works effectively even with moderate sample sizes. A pharmacokinetics study on renal cancer data is illustrated using the proposed method.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1194 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust approach for variable selection with high dimensional Logitudinal data analysis

This paper proposes a new robust smooth-threshold estimating equation to select important variables and automatically estimate parameters for high dimensional longitudinal data. A novel working correlation matrix is proposed to capture correlations within the same subject. The proposed procedure works well when the number of covariates p increases as the number of subjects n increases. The proposed estimates are competitive with the estimates obtained with the true correlation structure, especially when the data are contaminated. Moreover, the proposed method is robust against outliers in the response variables and/or covariates. Furthermore, the oracle properties for robust smooth-threshold estimating equations under "large n, diverging p" are established under some regularity conditions. Extensive simulation studies and a yeast cell cycle data are used to evaluate the performance of the proposed method, and results show that our proposed method is competitive with existing robust variable selection procedures.Comment: 32 pages, 7 tables, 5 figure

Fused lasso with the adaptation of parameter ordering in combining multiple studies with repeated measurements

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135531/1/biom12496.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135531/2/biom12496_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135531/3/biom12496-sup-0001-SuppData.pd

Development of Joint Estimating Equation Approaches to Merging Clustered or Longitudinal Datasets from Multiple Biomedical Studies.

Jointly analyzing multiple datasets arising from similar studies has drawn increasing attention in recent years. In this dissertation, we investigate three primary problems pertinent to merging clustered or longitudinal datasets from multiple biomedical studies. The first project concerns the development of a rigorous hypothesis testing procedure to assess the validity of data merging and a joint estimation approach to obtaining regression coefficient estimates when merging data is permitted. The proposed methods can account for different within-subject correlations and follow-up schedules in different longitudinal studies. The second project concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics, such as different follow-up schedules and study-specific missing covariates (e.g. covariates observed in some studies but completely missing in other studies). The presence of study-specific missing covariates gives rise to a great challenge in data merging and analysis, where methods of imputation and inverse probability weighting are not directly applicable. We propose a joint estimating function approach to addressing this key challenge, in which a novel nonparametric estimating function constructed via splines-based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates. Under mild regularity conditions, we show that the proposed estimator is consistent and asymptotically normal. The third project is devoted to the development of a screening procedure for parameter homogeneity, which is the key feature to reduce model complexity in the process of data merging. We consider the longitudinal marginal model for merged studies, in which the classical hypothesis testing approach to evaluating all possible subsets of common regression parameters can be combinatorially complex and computationally prohibitive. We develop a regularization method that can overcome this difficulty by applying the idea of adaptive fused lasso in that restrictions are imposed on differences of pairs of parameters between studies. The selection procedure will automatically detect common parameters across all or subsets of studies.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/95928/1/wafei_1.pd

Statistical Modelling

The book collects the proceedings of the 19th International Workshop on Statistical Modelling held in Florence on July 2004. Statistical modelling is an important cornerstone in many scientific disciplines, and the workshop has provided a rich environment for cross-fertilization of ideas from different disciplines. It consists in four invited lectures, 48 contributed papers and 47 posters. The contributions are arranged in sessions: Statistical Modelling; Statistical Modelling in Genomics; Semi-parametric Regression Models; Generalized Linear Mixed Models; Correlated Data Modelling; Missing Data, Measurement of Error and Survival Analysis; Spatial Data Modelling and Time Series and Econometrics

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis