Related papers: Simultaneous Selection of Optimal Bandwidths for t…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…
High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…
In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…
The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…
This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i)…
Regression discontinuity (RD) designs are a popular approach to estimating a treatment effect of cutoff-based interventions. Two current estimation approaches dominate the literature. One fits separate regressions on either side of the…
We provide a way to infer about existence of topological circularity in high-dimensional data sets in $\mathbb{R}^d$ from its projection in $\mathbb{R}^2$ obtained through a fast manifold learning map as a function of the high-dimensional…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…
This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack…
The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with…