Related papers: Linear functional estimation under multiplicative …

Let $\{X_n: n\in \N\}$ be a linear process with density function $f(x)\in L^2(\R)$. We study wavelet density estimation of $f(x)$. Under some regular conditions on the characteristic function of innovations, we achieve, based on the number…

We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…

Given an i.i.d. sample $X_1,...,X_n$ with common bounded density $f_0$ belonging to a Sobolev space of order $\alpha$ over the real line, estimation of the quadratic functional $\int_{\mathbb{R}}f_0^2(x) \mathrm{d}x$ is considered. It is…

Nonparametric kernel density estimation is a very natural procedure which simply makes use of the smoothing power of the convolution operation. Yet, it performs poorly when the density of a positive variable is to be estimated (boundary…

This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process.…

We study prediction in the functional linear model with functional outputs : $Y=SX+\epsilon $ where the covariates $X$ and $Y$ belong to some functional space and $S$ is a linear operator. We provide the asymptotic mean square prediction…

Let $X=\{X_n: n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator \[ \frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big) \] to…

Typical Bayesian inference requires parameter identification via likelihood parameterization, which has invited criticism for being less flexible than the Frequentist framework and subject to misspecification. Though misspecification may be…

Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance \cite{biau:16}), classification rules (see…

This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known…

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…

We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…

This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of the sequence with…

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

The present paper considers a problem of estimating a linear functional $\Phi=\int_{-\infty}^\infty \varphi(x) f(x)dx$ of an unknown deconvolution density $f$ on the basis of i.i.d. observations $Y_i = \theta_i + \xi_i$ where $\xi_i$ has a…

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…