Re-calibration of sample means

We consider the problem of calibration and the GREG method as suggested and studied in Deville and Sarndal (1992). We show that a GREG type estimator is typically not minimal variance unbiased estimator even asymptotically. We suggest a similar estimator which is unbiased but is asymptotically with a minimal variance

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities

L1pred: A Sequence-Based Prediction Tool for Catalytic Residues in Enzymes with the L1-logreg Classifier

To understand enzyme functions, identifying the catalytic residues is a usual first step. Moreover, knowledge about catalytic residues is also useful for protein engineering and drug-design. However, to experimentally identify catalytic residues remains challenging for reasons of time and cost. Therefore, computational methods have been explored to predict catalytic residues. Here, we developed a new algorithm, L1pred, for catalytic residue prediction, by using the L1-logreg classifier to integrate eight sequence-based scoring functions. We tested L1pred and compared it against several existing sequence-based methods on carefully designed datasets Data604 and Data63. With ten-fold cross-validation, L1pred showed the area under precision-recall curve (AUPR) and the area under ROC curve (AUC) of 0.2198 and 0.9494 on the training dataset, Data604, respectively. In addition, on the independent test dataset, Data63, it showed the AUPR and AUC values of 0.2636 and 0.9375, respectively. Compared with other sequence-based methods, L1pred showed the best performance on both datasets. We also analyzed the importance of each attribute in the algorithm, and found that all the scores contributed more or less equally to the L1pred performance

Variable selection for large p small n regression models with incomplete data: Mapping QTL with epistases

<p>Abstract</p> <p>Background</p> <p>Identifying quantitative trait loci (QTL) for both additive and epistatic effects raises the statistical issue of selecting variables from a large number of candidates using a small number of observations. Missing trait and/or marker values prevent one from directly applying the classical model selection criteria such as Akaike's information criterion (AIC) and Bayesian information criterion (BIC).</p> <p>Results</p> <p>We propose a two-step Bayesian variable selection method which deals with the sparse parameter space and the small sample size issues. The regression coefficient priors are flexible enough to incorporate the characteristic of "large <it>p </it>small <it>n</it>" data. Specifically, sparseness and possible asymmetry of the significant coefficients are dealt with by developing a Gibbs sampling algorithm to stochastically search through low-dimensional subspaces for significant variables. The superior performance of the approach is demonstrated via simulation study. We also applied it to real QTL mapping datasets.</p> <p>Conclusion</p> <p>The two-step procedure coupled with Bayesian classification offers flexibility in modeling "large p small n" data, especially for the sparse and asymmetric parameter space. This approach can be extended to other settings characterized by high dimension and low sample size.</p

The Poisson Compound Decision Problem Revisited

Abstract: The compound decision problem for a vector of independent Poisson random variables with possibly different means has half a century old solution. However, it appears that the classical solution needs smoothing adjustment even when there are many observations and relatively small means such that the empirical distribution is close to its mean. We discuss three such adjustments. We also present another approach that first transforms the problem into the normal compound decision problem. 1