Related papers: Varying Coefficient Model via Adaptive Spline Fitt…

Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…

Local variable selection aims to test for the effect of covariates on an outcome within specific regions. We outline a challenge that arises in the presence of non-linear effects and model misspecification. Specifically, for common…

Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions…

We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

We propose a novel approach to nonlinear functional regression, called the Mapping-to-Parameter function model, which addresses complex and nonlinear functional regression problems in parameter space by employing any supervised learning…

Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. This paper presents the…

Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…

This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…

We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$ type penalty is imposed to achieve…

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…

In semivarying coefficient models for longitudinal/clustered data, usually of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation…

In this paper, a new approach to solve the cubic B-spline curve fitting problem is presented based on a meta-heuristic algorithm called " dolphin echolocation ". The method minimizes the proximity error value of the selected nodes that…

In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

We consider a sparse high-dimensional varying coefficients model with random effects, a flexible linear model allowing covariates and coefficients to have a functional dependence with time. For each individual, we observe discretely sampled…

In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

This paper presents a new approach to selecting knots at the same time as estimating the B-spline regression model. Such simultaneous selection of knots and model is not trivial, but our strategy can make it possible by employing a…