Related papers: Some results on random design regression with long…
When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…
In this article, the analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator…
In rectangular-target pointing, movement angles towards targets are known to affect error rates. When designers determine target sizes, however, they would not know the frequencies of cursor-approaching directions for each target. Thus,…
We investigate random feature models in which neural networks sampled from a prescribed initialization ensemble are frozen and used as random features, with only the readout weights optimized. Adopting a statistical-physics viewpoint, we…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
This paper considers the Liu estimator in the multinomial logistic regression model. We propose some different estimators of the biasing parameter. The mean square error (MSE) is considered as the performance criterion. In order to compare…
We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and…
A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully…
Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
In this paper, we develop new multiscale methods to test qualitative hypotheses about the regression function m in a nonparametric regression model with fixed design points and time series errors. In time series applications, m represents a…
Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the…
We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales,…
We introduce the data driven extreme value distribution (DDEVD) estimator, a kernel-based method for estimating extreme value distributions from data. We derive its mean integrated squared error (MISE) in detail, use it to compute the…
In this paper, we deal with the data-driven selection of multidimensional and possibly anisotropic bandwidths in the general framework of kernel empirical risk minimization. We propose a universal selection rule, which leads to optimal…
In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression…
We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic…