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A fast and flexible $k$NN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…
We prove several results regarding the distribution of numbers that are the product of a prime and a $k$-th power. First, we prove an asymptotic formula for the counting function of such numbers; this generalises a result of E. Cohen. We…
We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which…
I summarize Density Functional Theory (DFT) in a language familiar to quantum field theorists, and introduce several apparently novel ideas for constructing {\it systematic} approximations for the density functional. I also note that, at…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
The Pitman sampling formula has been intensively studied as a distribution of random partitions. One of the objects of interest is the length $K (= K_{n,\theta,\alpha})$ of a random partition that follows the Pitman sampling formula, where…
In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
A common tool in Casimir physics (and many other areas) is the asymptotic (high-frequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions. Here we…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology…