Related papers: Methodology and theory for partial least squares a…
Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…
Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…
Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance…
This work aims to give non-asymptotic results for estimating the first principal component of a multivariate random process. We first define the covariance function and the covariance operator in the multivariate case. We then define a…
In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra…
Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In…
Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the…
This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More…
Partial diffusion scheme is an effective method for reducing computational load and power consumption in adaptive network implementation. The Information is exchanged among the nodes, usually over noisy links. In this paper, we consider a…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…