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Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…

Statistics Theory · Mathematics 2009-09-29 Anton Schick , Wolfgang Wefelmeyer

In this paper, we aim at estimating the quarticity of continuous It\^{o} semimartingales. Instead of using some classical estimators, we introduce a more intuitive one and establish a central limit theorem (CLT) for it, with a convergence…

Statistics Theory · Mathematics 2026-05-01 Yi Guo

In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ($\alpha N$) and sampled under two different random times. Based on…

Statistics Theory · Mathematics 2020-12-17 Tania Roa , Soledad Torres , Ciprian tudor

A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in…

Statistics Theory · Mathematics 2025-09-10 Chih-Wei Chen , Hau-Tieng Wu

We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to…

Computational Finance · Quantitative Finance 2015-03-19 Viorel Costeanu , Dan Pirjol

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…

Statistics Theory · Mathematics 2007-08-22 Ming-Yen Cheng , Liang Peng , Jyh-Shyang Wu

An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…

Statistics Theory · Mathematics 2014-07-02 Markus Bibinger , Nikolaus Hautsch , Peter Malec , Markus Reiß

We consider the problem of estimating smooth integrated functionals of a monotone nonincreasing density $f$ on $[0,\infty)$ using the nonparametric maximum likelihood based plug-in estimator. We find the exact asymptotic distribution of…

Statistics Theory · Mathematics 2019-04-16 Rajarshi Mukherjee , Bodhisattva Sen

This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal functions. A general upper bound for the nonasymptotic L_1-risk of the estimator is given. The method is applied to the shape respecting…

Statistics Theory · Mathematics 2007-06-13 L. Reboul

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood…

Statistics Theory · Mathematics 2009-06-12 Feike C. Drost , Ramon van den Akker , Bas J. M. Werker

We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is…

Machine Learning · Statistics 2014-10-31 Akshay Krishnamurthy , Kirthevasan Kandasamy , Barnabas Poczos , Larry Wasserman

Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…

Statistics Theory · Mathematics 2007-06-13 Peter Hall , Qiwei Yao

We prove non-asymptotic rates of convergence in the $W^{s,2}(\mathbb R^d)$-norm for the solution of the fractional Dirichlet problem to the solution of the local Dirichlet problem as $s\uparrow 1$. For regular enough boundary values we get…

Analysis of PDEs · Mathematics 2024-08-07 Leon Bungert , Félix del Teso

In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…

Statistics Theory · Mathematics 2024-06-17 Carsten Chong , Marc Hoffmann , Yanghui Liu , Mathieu Rosenbaum , Grégoire Szymanski

This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with…

Statistics Theory · Mathematics 2023-05-18 Marie Badreau , Frédéric Proïa

In this paper we study some asymptotic properties of the kernel conditional quantile estimator with randomly left-truncated data which exhibit some kind of dependence. We extend the result obtained by Lemdani, Ould-Sa\"id and Poulin [16] in…

Statistics Theory · Mathematics 2008-10-08 Elias Ould-Saïd , Djabrane Yahia , Abdelhakim Necir

This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…

Statistics Theory · Mathematics 2014-03-27 Zhengyuan Gao

This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…

Probability · Mathematics 2014-09-10 Mark Podolskij , Christian Schmidt , Johanna F. Ziegel

We consider a process $X^\ve$ that solves a stochastic Volterra equation with an unknown parameter $\theta^\star$ in the drift function. The Volterra kernel is singular, and includes as an example, $K\_0(u)=c u^{\alpha-1/2} \id{u>0}$ with…

Statistics Theory · Mathematics 2026-05-21 Arnaud Gloter , Nakahiro Yoshida

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…

Econometrics · Economics 2023-06-07 Haitian Xie