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Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariates, in this article, we first construct a tensor product space of reproducing kernel Hilbert spaces and build an analysis of variance (ANOVA) decomposition of the tensor product space. We then use a model selection method with the L 1 criterion to estimate the functional function with functional covariate inputs and detect interaction effects among the functional covariates. The proposed method is evaluated using simulations and stroke rehabilitation data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonconcave penalized M-estimation of the least absolute relative errors (penalized M-LARE) method for a sparse multiplicative regression model, where the dimension of model can increase with the sample size. Under certain appropriate conditions, the consistency and asymptotic normality for the penalized M-LARE estimator are established. Simulations and a real data analysis are in support of our theoretical results and illustrate that the proposed method performs well. [ABSTRACT FROM AUTHOR]

This research focuses on big experimental data analysis and the replenishment operation in a crane & shuttle based storage and retrieval system (C&SBS/RS). It is proposed that the order structure is expressed by three indicators: the order strength, the order size, and the order density. This aims to develop a regression function for the replenishment strategy to reveal the relationship between the order structure and replenishment parameters. The simulation model of the system is developed using FlexSim 7.1. A total of 13,440 combinations of order structures are provided as the simulation input. The statistical analyses are completed using the popular statistical software MINITAB. In this study, we use two different methods, best subset regression, and stepwise regression, to fit the regression function and find the best regression. According to the regression function, operation managers can develop better operation strategies. [ABSTRACT FROM AUTHOR]

The least product relative error (LPRE) estimator and test statistic to test linear hypotheses of regression parameters in the multiplicative regression model are studied when the number of covariate variables increases with the sample size. Some properties of the LPRE estimator and test statistic are obtained such as consistency, Bahadur presentation, and asymptotic distributions. Furthermore, we extend the LPRE to a more general relative error criterion and provide their statistical properties. Numerical studies including simulations and two real examples show that the proposed estimation performs well. [ABSTRACT FROM AUTHOR]

Autoregressive (AR) models with finite variance errors have been well studied. This paper is concerned with AR models with heavy-tailed errors, which is useful in various scientific research areas. Statistical estimation for AR models with infinite variance errors is very different from those for AR models with finite variance errors. In this paper, we consider a weighted quantile regression for AR models to deal with infinite variance errors. We further propose an induced smoothing method to deal with computational challenges in weighted quantile regression. We show that the difference between weighted quantile regression estimate and its smoothed version is negligible. We further propose a test for linear hypothesis on the regression coefficients. We conduct Monte Carlo simulation study to assess the finite sample performance of the proposed procedures. We illustrate the proposed methodology by an empirical analysis of a real-life data set. [ABSTRACT FROM AUTHOR]

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28–30, 1990, pp. 63–78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208–217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Mu¨ller estimator are provided. [Copyright &y& Elsevier]

In this paper, we work on a general multivariate regression model under the regime that both p , the number of covariates, and n , the number of observations, are large with p ∕ n → κ (0 < κ < ∞). Unlike previous works that focus on a sparse regression vector β , we consider a more interesting situation in which β is composed of two groups: components in group I are large while components in group II are small but possibly not zeros. This study aims to explore the asymptotic behavior of the ridge-regularized high-dimensional multivariate M-estimator of β in group II. By applying the double leave-one-out method, we successfully derive a nonlinear system comprised of two deterministic equations, which characterizes the risk behavior of the M-estimator. The system solution also enables us to yield asymptotic normality for each component of the M-estimator. Moreover, we present rigorous proofs to these approximations that play a critical role in deriving the system. Finally, we perform experimental validations to demonstrate the performance of the proposed system. [ABSTRACT FROM AUTHOR]