Related papers: Score estimation in the monotone single index mode…
The finite-dimensional parameters of the monotone single index model are often estimated by minimization of a least squares criterion and reparametrization to deal with the non-unicity. We avoid the reparametrization by using a…
We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…
We consider least squares estimators of the finite regression parameter $\alpha$ in the single index regression model $Y=\psi(\alpha^T X)+\epsilon$, where $X$ is a $d$-dimensional random vector, $\E(Y|X)=\psi(\alpha^T X)$, and where $\psi$…
We consider estimation and inference in a single index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least squares estimator (CLSE) for both the parametric and the nonparametric…
Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional…
We study the monotone single index model where a real response variable $Y $ is linked to a $d$-dimensional covariate $X$ through the relationship $E[Y | X] = \Psi_0(\alpha^T_0 X)$ almost surely. Both the ridge function, $\Psi_0$, and the…
We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the…
The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming $ \mathbb{E} [ Y | X ] = g(A^\top X) $ for some unknown index space $A$ and link function $g$. In this…
In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
This paper is concerned with model averaging estimation for partially linear functional score models. These models predict a scalar response using both parametric effect of scalar predictors and non-parametric effect of a functional…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index…
This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…
In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we…
We consider a high-dimensional monotone single index model (hdSIM), which is a semiparametric extension of a high-dimensional generalize linear model (hdGLM), where the link function is unknown, but constrained with monotone and…
This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…
We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensional structure, we prove that implicit score matching is able…
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…