Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. In this paper, we develop a regularisation method for estimating the covariance function and a stepwise procedure for estimating the parametric components efficiently in the varying-coefficient partially linear model. This procedure is also applicable to the varying-coefficient temporal mixed-effects model. Our method utilises the structure of the covariance function and thus has faster rates of convergence in estimating the covariance functions and outperforms the existing approaches in simulation studies. This procedure is easy to implement and its numerical performance is investigated using both simulated and real data.
This paper concerns statistical estimation of the partially linear model (PLM) for time course measurements, which are temporally correlated and allow multiple-run for repeated measurements to enhance experimental accuracy without extending the number of time points within each trial. Such features arise naturally from biomedical data in for e.g. brain fMRI and call for special treatment beyond classical methods in either a purely nonparametric regression model or a PLM with independent errors. We develop a stepwise procedure for estimating the parametric and nonparametric components of the multiple-run PLM and making inference for parameters of interest, adaptive to either single- or multiple-run, in the presence of error temporal dependence. Simulation study and real fMRI data applications illustrate the computational simplicity and effectiveness of the proposed methods. Supplementary material for this paper is available online.
AbstractThis article concerns statistical estimation of the partially linear model (PLM) for time course measurements, which are temporally correlated and allow multiple-runs for repeated measurements to enhance experimental accuracy without extending the number of time points within each trial. Such features arise naturally from biomedical data, for example, in brain fMRI, and call for special treatment beyond classical methods in either a purely nonparametric regression model or a PLM with independent errors. We develop a stepwise procedure for estimating the parametric and nonparametric components of the multiple-run PLM and making inference for parameters of interest, adaptive to either single- or multiple-run, in the presence of error temporal dependence. Simulation study and real fMRI data applications illustrate the computational simplicity and effectiveness of the proposed methods. Supplementary material for this article is available online.Key Words: Autocorrelation matrixDifference-based methodfMRIMatrix inverseMultiple testingSemiparametric model AcknowledgmentsThe authors thank the Associate Editor and an anonymous referee for insightful comments. Zhang's research is supported by the NSF grants DMS–1106586, DMS–1308872, and DMS--1521761, and Wisconsin Alumni Research Foundation. Han's research is supported by the Scientific Research Foundation of Northeast Dianli University (No. BSJXM-201216).Additional informationNotes on contributorsChunming ZhangChunming Zhang, School of Mathematical Sciences, Nankai University, Tianjin 300071, China; Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: cmzhang@stat.wisc.edu). Yu Han, School of Science, Northeast Dianli University, Jilin, Jilin 132013, P.R. China (E-mail: hanyu@mail.nedu.edu.cn). Shengji Jia, Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: shengji@stat.wisc.edu).Yu HanChunming Zhang, School of Mathematical Sciences, Nankai University, Tianjin 300071, China; Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: cmzhang@stat.wisc.edu). Yu Han, School of Science, Northeast Dianli University, Jilin, Jilin 132013, P.R. China (E-mail: hanyu@mail.nedu.edu.cn). Shengji Jia, Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: shengji@stat.wisc.edu).Shengji JiaChunming Zhang, School of Mathematical Sciences, Nankai University, Tianjin 300071, China; Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: cmzhang@stat.wisc.edu). Yu Han, School of Science, Northeast Dianli University, Jilin, Jilin 132013, P.R. China (E-mail: hanyu@mail.nedu.edu.cn). Shengji Jia, Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: shengji@stat.wisc.edu).
Knowing the number and the exact locations of multiple change points in genomic sequences serves several biological needs. The cumulative-segmented algorithm (cumSeg) has been recently proposed as a computationally efficient approach for multiple change-points detection, which is based on a simple transformation of data and provides results quite robust to model mis-specifications. However, the errors are also accumulated in the transformed model so that heteroscedasticity and serial correlation will show up, and thus the variations of the estimated change points will be quite different, while the locations of the change points should be of the same importance in the original genomic sequences.In this study, we develop two new change-points detection procedures in the framework of cumulative segmented regression. Simulations reveal that the proposed methods not only improve the efficiency of each change point estimator substantially but also provide the estimators with similar variations for all the change points. By applying these proposed algorithms to Coriel and SNP genotyping data, we illustrate their performance on detecting copy number variations.The proposed algorithms are implemented in R program and the codes are provided in the online supplementary material.Supplementary data are available at Bioinformatics online.
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