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In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…
We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…
We consider the problem of estimating the value l({\phi}) of a linear functional, where the structural function {\phi} models a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based…
We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
In this paper, we study the functional linear multiplicative model based on the least product relative error criterion. Under some regularization conditions, we establish the consistency and asymptotic normality of the estimator. Further,…
This work concerns the estimation of multidimensional nonlinear regression models using multilayer perceptrons (MLPs). The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator.…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
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…
We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…
Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function,…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
We study semiparametric inference in some linear regression models with time-varying coefficients, dependent regressors and dependent errors. This problem, which has been considered recently by Zhang and Wu (2012) under the functional…