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
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References

SHOWING 1-10 OF 33 REFERENCES
Pointwise adaptive estimation of a multivariate density under independence hypothesis
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 pointwiseExpand
Functional Estimation of a Density Under a New Weak Dependence Condition
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
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 presentExpand
Adaptive pointwise estimation of conditional density function
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 theExpand
Convolution power kernels for density estimation
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. TheExpand
Lp adaptive density estimation in a β mixing framework
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 riskExpand
Adaptive estimation of conditional density function
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 theExpand
Pointwise adaptive estimation of a multivariate function
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) theExpand
Exact adaptive pointwise estimation on Sobolev classes of densities
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 theExpand
Convergence rates for density estimators of weakly dependent time series
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 $f$. WeExpand
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