# Pointwise Adaptive Estimation of the MarginalDensity of a Weakly Dependent Process

@article{Bertin2016PointwiseAE, title={Pointwise Adaptive Estimation of the MarginalDensity of a Weakly Dependent Process}, author={Karine Bertin and N. Klutchnikoff}, journal={arXiv: Statistics Theory}, year={2016} }

This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth is selected using the approach of Goldenshluger and Lepski and we prove that the resulting estimator satisfies an oracle type inequality. The procedure is also proved to be adaptive (in a minimax framework) over a scale of H\"older balls for several types of… Expand

#### Tables from this paper

#### 3 Citations

Adaptive nonparametric estimation in the presence of dependence

- Mathematics
- 2016

ABSTRACT We consider nonparametric estimation problems in the presence of dependent data, notably nonparametric regression with random design and nonparametric density estimation. The proposed… Expand

Adaptive estimation for stochastic damping Hamiltonian systems under partial observation

- Mathematics
- 2017

Abstract The paper considers a process Z t = ( X t , Y t ) where X t is the position of a particle and Y t its velocity, driven by a hypoelliptic bi-dimensional stochastic differential equation.… Expand

Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion

- Mathematics
- 2020

We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete… Expand

#### References

SHOWING 1-10 OF 33 REFERENCES

Pointwise adaptive estimation of a multivariate density under independence hypothesis

- Mathematics
- 2015

In this paper, we study the problem of pointwise estimation of a multivariate density. We provide a data-driven selection rule from the family of kernel estimators and derive for it a pointwise… Expand

Functional Estimation of a Density Under a New Weak Dependence Condition

- Mathematics
- 2001

The purpose of this paper is to prove, through the analysis of the behaviour of a standard kernel density estimator, that the notion of weak dependence defined in a previous paper (cf. Doukhan &… Expand

Adaptive estimation of the stationary density of discrete and continuous time mixing processes

- Mathematics
- 2002

In this paper, we study the problem of non parametric estimation of the stationary mar- ginal density f of an or a -mixing process, observed either in continuous time or in discrete time. We present… Expand

Adaptive pointwise estimation of conditional density function

- Mathematics
- 2013

In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the… Expand

Convolution power kernels for density estimation

- Mathematics
- 2012

We propose a new type of non-parametric density estimators fitted to random variables with lower or upper-bounded support. To illustrate the method, we focus on nonnegative random variables. The… Expand

Lp adaptive density estimation in a β mixing framework

- Mathematics
- 1998

Abstract We study the L π − i n t e g r a t e d risk with π ≥ 2 of an adaptive density estimator by wavelets method for absolutely regular observations. By a duality argument, the study of the risk… Expand

Adaptive estimation of conditional density function

- Mathematics
- 2013

In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the… Expand

Pointwise adaptive estimation of a multivariate function

- Mathematics
- 2014

In this paper, we address the problem of pointwise estimation in the Gaussian white noise model. We propose a new data-driven procedure that achieves (up to a multiplicative logarithmic term) the… Expand

Exact adaptive pointwise estimation on Sobolev classes of densities

- Mathematics
- 2001

The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point , over the… Expand

Convergence rates for density estimators of weakly dependent time series

- Mathematics
- 2006

Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common marginal distribution admitting a density $f$, our aim is to provide a wide range of consistent estimators of $f$. We… Expand