Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Guntuboyina, Adityanand"'
The Grenander estimator is a well-studied procedure for univariate nonparametric density estimation. It is usually defined as the Maximum Likelihood Estimator (MLE) over the class of all non-increasing densities on the positive real line. It can also
Externí odkaz:
http://arxiv.org/abs/2410.10251
Publikováno v:
Ann. Statist. 52 (3) 1102 - 1126, June 2024
Multivariate adaptive regression splines (MARS) is a popular method for nonparametric regression introduced by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural lasso variant of
Externí odkaz:
http://arxiv.org/abs/2111.11694
Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior distribut
Externí odkaz:
http://arxiv.org/abs/2109.03466
Mixture of regression models are useful for regression analysis in heterogeneous populations where a single regression model may not be appropriate for the entire population. We study the nonparametric maximum likelihood estimator (NPMLE) for fitting
Externí odkaz:
http://arxiv.org/abs/2108.09816
We prove minimax bounds for estimating Gaussian location mixtures on $\mathbb{R}^d$ under the squared $L^2$ and the squared Hellinger loss functions. Under the squared $L^2$ loss, we prove that the minimax rate is upper and lower bounded by a constan
Externí odkaz:
http://arxiv.org/abs/2012.00444
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well defined with o
Externí odkaz:
http://arxiv.org/abs/2007.15252
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least Squares in est
Externí odkaz:
http://arxiv.org/abs/2006.04046
Under the usual nonparametric regression model with Gaussian errors, Least Squares Estimators (LSEs) over natural subclasses of convex functions are shown to be suboptimal for estimating a $d$-dimensional convex function in squared error loss when th
Externí odkaz:
http://arxiv.org/abs/2006.02044
Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of $k$ unknown affine functions for a fixed $k \geq 1$. This generalizes linear regression and (real) phase retrieval, and is closely related to con
Externí odkaz:
http://arxiv.org/abs/1906.09255
We consider the problem of nonparametric regression when the covariate is $d$-dimensional, where $d \geq 1$. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in this setting---the entirely monotonic LSE and the c
Externí odkaz:
http://arxiv.org/abs/1903.01395