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Full-Text Articles in Physical Sciences and Mathematics
Penalized Smoothed Partial Rank Estimator For The Nonparametric Transformation Survival Model With High-Dimensional Covariates, Wei Dai, Yi Li
Penalized Smoothed Partial Rank Estimator For The Nonparametric Transformation Survival Model With High-Dimensional Covariates, Wei Dai, Yi Li
The University of Michigan Department of Biostatistics Working Paper Series
Microarray technology has the potential to lead to a better understanding of biological processes and diseases such as cancer. When failure time outcomes are also available, one might be interested in relating gene expression profiles to the survival outcome such as time to cancer recurrence or time to death. This is statistically challenging because the number of covariates greatly exceeds the number of observations. While the majority of work has focused on regularized Cox regression model and accelerated failure time model, they may be restrictive in practice. We relax the model assumption and and consider a nonparametric transformation model that …
Ultrahigh Dimensional Time Course Feature Selection, Peirong Xu, Lixing Zhu, Yi Li
Ultrahigh Dimensional Time Course Feature Selection, Peirong Xu, Lixing Zhu, Yi Li
The University of Michigan Department of Biostatistics Working Paper Series
Statistical challenges arise from modern biomedical studies that produce time course genomic data with ultrahigh dimensions. In a renal cancer study that motivated this paper, the pharmacokinetic measures of a tumor suppressor (CCI-779) and expression levels of 12625 genes were measured for each of 33 patients at 8 and 16 weeks after the start of treatments, with the goal of identifying predictive gene transcripts and the interactions with time in peripheral blood mononuclear cells for pharmacokinetics over the time course. The resulting dataset defies analysis even with regularized regression. Although some remedies have been proposed for both linear and generalized …
Covariance-Enhanced Discriminant Analysis, Peirong Xu, Ji Zhu, Lixing Zhu, Yi Li
Covariance-Enhanced Discriminant Analysis, Peirong Xu, Ji Zhu, Lixing Zhu, Yi Li
The University of Michigan Department of Biostatistics Working Paper Series
Linear discriminant analysis (LDA), a classical method in pattern recognition and machine learning, has been widely used to characterize or separate multiple classes via linear combinations of features. However, the high-dimensionality of the high-throughput features obtained from modern biological experiments, for example, microarray or proteomics, defies traditional discriminant analysis techniques. The possible interfeature correlations present additional challenges and are often under-utilized in modeling. In this paper, by incorporating the possible inter-feature correlations, we propose a Covariance-Enhanced Discriminant Analysis (CEDA) method that simultaneously and consistently selects informative features and identifies the corresponding discriminable classes. We show that, under mild regularity conditions, …
Sparse Ridge Fusion For Linear Regression, Nozad Mahmood
Sparse Ridge Fusion For Linear Regression, Nozad Mahmood
Electronic Theses and Dissertations
For a linear regression, the traditional technique deals with a case where the number of observations n more than the number of predictor variables p (n > p). In the case n < p, the classical method fails to estimate the coefficients. A solution of the problem is the case of correlated predictors is provided in this thesis. A new regularization and variable selection is proposed under the name of Sparse Ridge Fusion (SRF). In the case of highly correlated predictor, the simulated examples and a real data show that the SRF always outperforms the lasso, eleastic net, and the S-Lasso, and the results show that the SRF selects more predictor variables than the sample size n while the maximum selected variables by lasso is n size.
Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang
Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang
Research Collection School Of Economics
This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD) or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.