Related papers: Nonparametric estimation of composite functions
We present and study semi-parametric estimators for the mean of functional outcomes in situations where some of these outcomes are missing and covariate information is available on all units. Assuming that the missingness mechanism depends…
The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space.…
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…
We study the minimax estimation of covariance eigenfunctions and eigenvalues in functional principal component analysis when $n$ trajectories are observed at $p$ common grid points with additive noise. We consider covariance kernels with…
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
We consider the problem of adaptive estimation of the functional component in a multivariate partial linear model where the argument of the function is defined on a $q$-dimensional grid. Obtaining an adaptive estimator of this functional…
We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true…
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is only observed on a subinterval of length $\delta<1$, one has no…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…
The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations…
This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…