Related papers: On a Nadaraya-Watson Estimator with Two Bandwidths
Let $i=1,\ldots,N$ index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors $X_{i}$ and, for each of the $N\left(N-1\right)$ ordered pairs of units, an outcome $Y_{ij}$. The…
In this paper we propose an automatic selection of the bandwidth of the semi-recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and some…
This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain…
A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and…
We study the Nadaraya-Watson (N-W) estimator for the drift function of two-sided reflected stochastic processes. We propose a discrete-type N-W estimator and a continuous-type N-W estimator based on the discretely observed processes and…
Associated kernels have been introduced to improve the classical continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. This work deals with the effects of combined…
It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same…
We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…
In this paper we prove large deviations principles for the Nadaraya-Watson estimator of the regression of a real-valued variable with a functional covariate. Under suitable conditions, we show pointwise and uniform large deviations theorems…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
This paper is devoted to the nonparametric estimation of the derivative of the regression function in a nonparametric regression model. We implement a very efficient and easy to handle statistical procedure based on the derivative of the…
The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This…
Most machine learning methods require tuning of hyper-parameters. For kernel ridge regression with the Gaussian kernel, the hyper-parameter is the bandwidth. The bandwidth specifies the length scale of the kernel and has to be carefully…
This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…
We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the…
Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model…
This paper deals with a nonparametric Nadaraya-Watson estimator $\hat b$ of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on $\hat b$ and its discrete-time approximation are…
In recent years, there has been much interest in understanding the generalization behavior of interpolating predictors, which overfit on noisy training data. Whereas standard analyses are concerned with whether a method is consistent or…
This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro…