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Full-Text Articles in Statistical Models
Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan
Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …
Unified Cross-Validation Methodology For Selection Among Estimators And A General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities And Examples, Mark J. Van Der Laan, Sandrine Dudoit
Unified Cross-Validation Methodology For Selection Among Estimators And A General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities And Examples, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
In Part I of this article we propose a general cross-validation criterian for selecting among a collection of estimators of a particular parameter of interest based on n i.i.d. observations. It is assumed that the parameter of interest minimizes the expectation (w.r.t. to the distribution of the observed data structure) of a particular loss function of a candidate parameter value and the observed data structure, possibly indexed by a nuisance parameter. The proposed cross-validation criterian is defined as the empirical mean over the validation sample of the loss function at the parameter estimate based on the training sample, averaged over …
Asymptotically Optimal Model Selection Method With Right Censored Outcomes, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit
Asymptotically Optimal Model Selection Method With Right Censored Outcomes, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
Over the last two decades, non-parametric and semi-parametric approaches that adapt well known techniques such as regression methods to the analysis of right censored data, e.g. right censored survival data, became popular in the statistics literature. However, the problem of choosing the best model (predictor) among a set of proposed models (predictors) in the right censored data setting have not gained much attention. In this paper, we develop a new cross-validation based model selection method to select among predictors of right censored outcomes such as survival times. The proposed method considers the risk of a given predictor based on the …
Tree-Based Multivariate Regression And Density Estimation With Right-Censored Data , Annette M. Molinaro, Sandrine Dudoit, Mark J. Van Der Laan
Tree-Based Multivariate Regression And Density Estimation With Right-Censored Data , Annette M. Molinaro, Sandrine Dudoit, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We propose a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. This approach is entirely driven by the choice of a loss function for the full (uncensored) data structure and can be stated in terms of the following three main steps. (1) Define the parameter of interest as the minimizer of the expected loss, or risk, for a full data loss function chosen to represent the desired measure of performance. Map the full data loss function into an observed (censored) data loss function having the same expected value and leading to an efficient estimator …
A Semiparametric Model Selection Criterion With Applications To The Marginal Structural Model, M. Alan Brookhart, Mark J. Van Der Laan
A Semiparametric Model Selection Criterion With Applications To The Marginal Structural Model, M. Alan Brookhart, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Estimators for the parameter of interest in semiparametric models often depend on a guessed model for the nuisance parameter. The choice of the model for the nuisance parameter can affect both the finite sample bias and efficiency of the resulting estimator of the parameter of interest. In this paper we propose a finite sample criterion based on cross validation that can be used to select a nuisance parameter model from a list of candidate models. We show that expected value of this criterion is minimized by the nuisance parameter model that yields the estimator of the parameter of interest with …