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In this paper, we propose a frequentist model averaging method for quantile regression with high‐dimensional covariates. Although research on these subjects has proliferated as separate approaches, no study has considered them in conjunction. Our method entails reducing the covariate dimensions through ranking the covariates based on marginal quantile utilities. The second step of our method implements model averaging on the models containing the covariates that survive the screening of the first step. We use a delete‐one cross‐validation method to select the model weights, and prove that the resultant estimator possesses an optimal asymptotic property uniformly over any compact (0,1) subset of the quantile indices. Our proof, which relies on empirical process theory, is arguably more challenging than proofs of similar results in other contexts owing to the high‐dimensional nature of the problem and our relaxation of the conventional assumption of the weights summing to one. Our investigation of finite‐sample performance demonstrates that the proposed method exhibits very favorable properties compared to the least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD) penalized regression methods. The method is applied to a microarray gene expression data set. [ABSTRACT FROM AUTHOR]

Outliers often occur during data collection, which could impact the result seriously and lead to a large inference error; therefore, it is important to detect outliers before data analysis. Gamma distribution is a popular distribution in statistics; this paper proposes a method for detecting multiple upper outliers from gamma ( m , θ ). For computing the critical value of the test statistic in our method, we derive the density function for the case of a single outlier and design two algorithms based on the Monte Carlo and the kernel density estimation for the case of multiple upper outliers. A simulation study shows that the test statistic proposed in this paper outperforms some common test statistics. Finally, we propose an improved testing method to reduce the impact of the swamping effect, which is demonstrated by real data analyses. [ABSTRACT FROM AUTHOR]

The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation criterion is minimized. We prove that the resultant combined-kernel estimator achieves the smallest possible asymptotic aggregate squared error. The superiority of the new estimator over estimators based on widely accepted conventional bandwidth choices in finite samples is demonstrated in a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

DNA pooling is a cost-effective approach for collecting information on marker allele frequency in genetic studies. It is often suggested as a screening tool to identify a subset of candidate markers from a very large number of markers to be followed up by more accurate and informative individual genotyping. In this article, we investigate several statistical properties and design issues related to this two-stage design, including the selection of the candidate markers for second-stage analysis, statistical power of this design, and the probability that truly disease-associated markers are ranked among the top after second-stage analysis. We have derived analytical results on the proportion of markers to be selected for second-stage analysis. For example, to detect disease-associated markers with an allele frequency difference of 0.05 between the cases and controls through an initial sample of 1000 cases and 1000 controls, our results suggest that when the measurement errors are small (0.005), ~3% of the markers should be selected. For the statistical power to identify disease-associated markers, we find that the measurement errors associated with DNA pooling have little effect on its power. This is in contrast to the one-stage pooling scheme where measurement errors may have large effect on statistical power. As for the probability that the disease-associated markers are ranked among the top in the second stage, we show that there is a high probability that at least one disease-associated marker is ranked among the top when the allele frequency differences between the cases and controls are not

With respect to the multiple-tests problem, recently an increasing amount of attention has been paid to control the false discovery rate (FDR), the positive false discovery rate (pFDR), and the proportion of false positives (PFP). The new approaches are generally believed to be more powerful than the classical Bonferroni one. This article focuses on the PFP approach. It demonstrates via examples in genetic association studies that the Bonferroni procedure can be more powerful than the PFP-control one and also shows the intrinsic connection between controlling the PFP and controlling the overall type I error rate. Since controlling the PFP does not necessarily lead to a desired power level, this article addresses the design issue and recommends the sample sizes that can attain the desired power levels when the PFP is controlled. The results in this article also provide rough guidance for the sample sizes to achieve the desired power levels when the FDR and especially the pFDR are controlled.