Related papers: Uniform convergence rates over maximal domains in …
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…
Discrete supervised learning problems such as classification are often tackled by introducing a continuous surrogate problem akin to regression. Bounding the original error, between estimate and solution, by the surrogate error endows…
We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and…
This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting…
Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…
In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…
Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the ``curse of dimensionality.'' Under rather weak conditions, we…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models…
This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
We study the consistency of the $k$-nearest neighbor regressor under complex survey designs. While consistency results for this algorithm are well established for independent and identically distributed data, corresponding results for…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
Von Neumann's original proof of the ergodic theorem is revisited. A uniform convergence rate is established under the assumption that one can control the density of the spectrum of the underlying self-adjoint operator when restricted to…
In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of…
This paper derives new asymptotic results for the adaptive LASSO estimator in cointegrating regressions, allowing for uncertainty about whether the regressors are exact unit root processes. We study model selection probabilities, estimator…
The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…