Distributed and parallel computing is becoming more important with the availability of extremely large data sets. In this article, we consider problem for high-dimensional linear quantile regression. We work under assumption that coefficients in regression model are sparse; therefore, a LASSO penalty naturally used estimation. first extend debiasing procedure, which previously proposed smooth parametric models to The technical challenges include dealing nondifferentiability loss function...

When predicting scalar responses in the situation where explanatory variables are functions, it is sometimes case that some functional related to linearly while other have more complicated relationships with responses. In this paper, we propose a new semi-parametric model take advantage of both parametric and nonparametric modelling. Asymptotic properties proposed estimators established finite sample behaviour investigated through small simulation experiment.

A single-index model (SIM) provides for parsimonious multidimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (nonlinear) models. We show that a particular Gaussian process (GP) formulation is simple to work and ideal as an emulator some types of computer experiment it can outperform the canonical separable GP commonly used in this setting. Our contribution focuses on drastically simplifying, reinterpreting, then generalizing recently...

Let (X1,Y1),…,(Xn,Yn) be independent and identically distributed random elements taking values in ℱ×ℋ, where ℱ is a semi-metric space ℋ separable Hilbert space. We investigate the rates of strong (almost sure) convergence k-nearest neighbor estimate. give two results assuming finite moment condition exponential tail on noises respectively, with latter requiring less stringent conditions k for convergence.

In this paper, we discuss a fully Bayesian quantile inference using Markov Chain Monte Carlo (MCMC) method for longitudinal data models with random effects. Under the assumption of error term subject to asymmetric Laplace distribution, establish hierarchical model and obtain posterior distribution unknown parameters at τ-th level. We overcome current computational limitations two approaches. One is general MCMC technique Metropolis–Hastings algorithm another Gibbs sampling from full...

This paper considers the estimation of sparse additive quantile regression (SAQR) in high-dimensional settings. Given nonsmooth nature loss function and nonparametric complexities component estimation, it is challenging to analyze theoretical properties ultrahigh-dimensional SAQR. We propose a regularized learning approach with two-fold Lasso-type regularization reproducing kernel Hilbert space (RKHS) for establish nonasymptotic oracle inequalities excess risk proposed estimator without any...

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of and lag order are even moderately large. This article proposes to rearrange transition matrices into tensor form such that parameter space can be restricted along three directions simultaneously via decomposition. In contrast, reduced-rank regression method restrict in only one direction. Besides achieving substantial dimension...

Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose novel Factor Augmented Single-Index Model. We first the concern whether it is necessary to consider augmented part by introducing score-type test statistic. Compared previous statistics, our proposed statistic does not need estimate high-dimensional coefficients, nor precision matrix, making...

Distributed frameworks for statistical estimation and inference have become a critical toolkit analyzing massive data efficiently. In this paper, we present distributed high-dimensional quantile regression with ℓ0 constraint using iterative hard thresholding (IHT). We propose communication-efficient estimator which is linearly convergent to the true parameter up precision of model, despite fact that check loss minimization problem an neither strongly smooth nor convex. The develop can...

High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of loss brings great challenges computation. To solve this critical issue, convoluted has been recently proposed, introducing estimators. these developed estimators cannot be directly used make inference. In paper, we investigate statistical inference problem regression. The use U-statistic in function presents analysis....

Abstract The author proposes an extension of reproducing kernel Hilbert space theory which provides a new framework for analyzing functional responses with regression models. approach only presumes general nonlinear structure, as opposed to existing linear generalized cross‐validation automatic smoothing parameter estimation. He illustrates the use estimator both on real and simulated data.

In this paper, we consider the problem of variable selection for high- dimensional generalized varying-coefficient models and propose a polynomial-spline based procedure that simultaneously eliminates irrelevant predictors estimates nonzero coefficients. large p, small n setting, demonstrate conver- gence rates estimator under suitable regularity assumptions. particular, show adaptive group lasso can correctly select important vari- ables with probability approaching one convergence...

We propose a new statistics for the detection of differentially expressed genes when are activated only in subset samples. Statistics designed this unconventional circumstance has proved to be valuable most cancer studies, where oncogenes small number disease Previous efforts made direction include outlier profile analysis (Tomlins and others, 2005), sum (Tibshirani Hastie, 2007), robust t-statistics (Wu, 2007). called maximum ordered (MOST) which seems natural samples is unknown. compare...

Functional linear regression is a useful extension of simple re- gression and has been investigated by many researchers. However, the functional variable selection problem when multiple observations exist, which counterpart in context regression, seldom stud- ied. Here we propose method using group smoothly clipped absolute deviation penalty (gSCAD) can perform estimation simultaneously. We show identify true model consistently, discuss construction pointwise confidence intervals for...

In this article, we propose a model selection and semiparametric estimation method for additive models in the context of quantile regression problems. particular, are interested finding nonzero components as well linear conditional function. Our approach is based on spline approximation aided by two Smoothly Clipped Absolute Deviation (SCAD) penalty terms. The advantage our that one can automatically choose between general models, partially single step. most important contribution achieved...