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In this paper, a minimizing average check loss estimation (MACLE) procedure is proposed for the single-index coefficient model (SICM) in the framework of quantile regression (QR). The resulting estimators have the asymptotic normality and achieve the best convergence rate. Furthermore, a variable selection method is investigated for the QRSICM by combining MACLE method with the adaptive LASSO penalty, and we also established the oracle property of the proposed variable selection method. Extensive simulations are conducted to assess the finite sample performance of the proposed estimation and variable selection procedure under various error settings. Finally, we present a real-data application of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider how to yield a robust empirical likelihood estimation for regression models. After introducing modal regression, we propose a novel empirical likelihood method based on modal regression estimation equations, which has the merits of both robustness and high inference efficiency compared with the least square based methods. Under some mild conditions, we show that Wilks' theorem of the proposed empirical likelihood approach continues to hold. Advantages of empirical likelihood modal regression as a nonparametric approach are illustrated by constructing confidence intervals/regions. Two simulation studies and a real data analysis confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

Partial linear single-index model (PLSIM) is a flexible and applicable model when investigating the underlying relationship between the response and the multivariate covariates. Most previous studies on PLSIM concentrated on mean regression, based on least square or likelihood approach. In contrast to this method, in this paper, we propose minimizing average check loss estimation (MACLE) procedure to conduct quantile regression of PLSIM. We construct an initial consistent quantile regression estimator of the parametric part base multi-dimensional kernels, and further promote the estimation efficiency to the optimal rate. We discuss the optimal bandwidth selection method and establish the asymptotic normality of the proposed MACLE estimators. Furthermore, we consider an adaptive lasso penalized variable selection method and establish its oracle property. Simulation studies with various distributed error and a real data analysis are conducted to show the promise of our proposed methods. [ABSTRACT FROM AUTHOR]

In many applications, covariates can be naturally grouped. For example, for gene expression data analysis, genes belonging to the same pathway might be viewed as a group. This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped. A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level. For the situations in which the number of parameters tends to ∞ as the sample size increases, we establish an oracle property and asymptotic normality property of the proposed estimators. Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso, smoothly clipped absolute deviation (SCAD) and adaptive lasso. [ABSTRACT FROM AUTHOR]

Semiparametric partially linear varying coefficient models (SPLVCM) are frequently used in statistical modeling. With high-dimensional covariates both in parametric and nonparametric part for SPLVCM, sparse modeling is often considered in practice. In this paper, we propose a new estimation and variable selection procedure based on modal regression, where the nonparametric functions are approximated by $$B$$ -spline basis. The outstanding merit of the proposed variable selection procedure is that it can achieve both robustness and efficiency by introducing an additional tuning parameter (i.e., bandwidth $$h$$ ). Its oracle property is also established for both the parametric and nonparametric part. Moreover, we give the data-driven bandwidth selection method and propose an EM-type algorithm for the proposed method. Monte Carlo simulation study and real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and real data analysis confirm that the newly proposed method works very well. [ABSTRACT FROM AUTHOR]

Abstract: As a useful supplement to mean regression, quantile regression is a completely distribution-free approach and is more robust to heavy-tailed random errors. In this paper, a variable selection procedure for quantile varying coefficient models is proposed by combining local polynomial smoothing with adaptive group LASSO. With an appropriate selection of tuning parameters by the BIC criterion, the theoretical properties of the new procedure, including consistency in variable selection and the oracle property in estimation, are established. The finite sample performance of the newly proposed method is investigated through simulation studies and the analysis of Boston house price data. Numerical studies confirm that the newly proposed procedure (QKLASSO) has both robustness and efficiency for varying coefficient models irrespective of error distribution, which is a good alternative and necessary supplement to the KLASSO method. [Copyright &y& Elsevier]

Discusses the measurement of isotopes using the cathodoluminescence imaging and ion microprobe zircon dating, at the uppermost Cretaceous Furao Formation near the Heilong River in China. Features of zircons; Outcrop of the Furaoan Stage in Baitoushan Section; Estimate of the formation age.