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未知分布加性噪声下的数据驱动密度估计AI 解读

Summary We study the model Y = X+ε. We assume that we have at our disposal independent identically distributed observations Y1,…,Yn and ε−1,…,ε−M. The (Xj)1 ⩽j ⩽n are independent identically distributed with density f, independent of the (εj)1 ⩽j ⩽n, independent identically distributed with density f. The aim of the paper is to estimate f without knowing f. We first define an estimator, for which we provide bounds for the integrated L2-risk. We consider ordinary smooth and…

离散时间随机波动率模型动态的自适应估计AI 解读

This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)[eta]i, Xi+1=b(Xi)+[sigma](Xi)[xi]i+1, where only (Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+[epsilon]i, Xi+1=b(Xi)+[sigma](Xi)[xi]i+1, where ([xi]i) and ([epsilon]i) are independent sequences of i.i.d. noise. Moreover, the sequences (Xi) and ([epsilon]i) are independent and the distribution of [epsilon] is known. Then, our aim is to estimate the functions…

一般 ARCH 模型的自适应密度估计AI 解读

We consider a model Y t = σ t η 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 t 2 ) based on the observations Y t . Under a new dependence structure, the τ-dependency defined by Dedecker and Prieur (2005, Probability Theory and Related Fields 132, 203–236), we prove that the rates of this nonparametric estimator…

通过模型选择实现自回归或 β 混合回归中的自适应估计AI 解读

We study the problem of estimatingsome unknown regression function in a $\beta$-mixing dependent framework. To this end, we consider some collection of models which are finite dimensional spaces. A penalized least-squares estimator (PLSE) is built on a data driven selected model among this collection. We state non asymptotic risk bounds for this PLSE and give several examples where the procedure can be applied (autoregression, regression with arithmetically $\beta$-mixing…

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连续时间模型中的非因果性AI 解读

In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as…