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Jérôme Dedecker

Publications and source records attributed to Jérôme Dedecker.

42 records · Page 3Linked to original sources
arXiv2011

Invariance principles for linear processes with application to isotonic regression

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range dependence and the limiting distribution is a fractional Brownian motion. The proofs are based on new approximations by a linear process with martingale difference innovations. The results are then applied to study an estimator of the isotonic regression when the error process is a (possibly long-range dependent) time series.

math.ST↗
arXiv2008

On mean central limit theorems for stationary sequences

In this paper, we give estimates of the minimal ${\mathbb{L}}^1$ distance between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.

math.PR↗
arXiv2007

Moderate deviations for stationary sequences of bounded random variables

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $ϕ$-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.

math.PR↗
arXiv2006

Adaptive density estimation for general ARCH models

We consider a model $Y\_t=σ\_tη\_t$ in which $(σ\_t)$ is not independent of the noise process $(η\_t)$, but $σ\_t$ is independent of $η\_t$ for each $t$. We assume that $(σ\_t)$ is stationary and we propose an adaptive estimator of the density of $\ln(σ^2\_t)$ based on the observations $Y\_t$. Under various dependence structures, the rates of this nonparametric estimator coincide with the minimax rates obtained in the i.i.d. case when $(σ\_t)$ and $(η\_t)$ are independent, in all cases where these minimax rates are known. The results apply to various linear and non linear ARCH processes.

math.ST↗
arXiv2006

Adaptive density deconvolution with dependent inputs

In the convolution model $Z\_i=X\_i+ ε\_i$, we give a model selection procedure to estimate the density of the unobserved variables $(X\_i)\_{1 \leq i \leq n}$, when the sequence $(X\_i)\_{i \geq 1}$ is strictly stationary but not necessarily independent. This procedure depends on wether the density of $ε\_i$ is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most classes of regularity on ${\mathbb R}$. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are super smooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence $(X\_i)\_{i \geq 1}$ is not a long-memory process.

math.ST↗