Related papers: Uniform asymptotics for kernel density estimators …
We evaluate asymptotically the variance of the number of squarefree integers up to $x$ in short intervals of length $H < x^{6/11 - \varepsilon}$ and the variance of the number of squarefree integers up to $x$ in arithmetic progressions…
In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…
Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalized discrete associated-kernel estimator of a probability mass function. We show, under…
In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function…
Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the…
We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…
We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the $d$-dimensional simplex. The simplex is an important case as…
This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to…
We study the asymptotic behaviour of needlets-based approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. We prove consistency and asymptotic Gaussianity, in the…
Given an i.i.d. sample $X_1,...,X_n$ with common bounded density $f_0$ belonging to a Sobolev space of order $\alpha$ over the real line, estimation of the quadratic functional $\int_{\mathbb{R}}f_0^2(x) \mathrm{d}x$ is considered. It is…
We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
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…
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…