Related papers: Linear functional estimation under multiplicative …
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…
The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
Imbalanced classification tasks are widespread in many real-world applications. For such classification tasks, in comparison with the accuracy rate, it is usually much more appropriate to use non-decomposable performance measures such as…
We study nonparametric estimation of univariate cumulative distribution functions (CDFs) pertaining to data missing at random. The proposed estimators smooth the inverse probability weighted (IPW) empirical CDF with the Bernstein operator,…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…
Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…
We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…
We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=\theta(t) X_tdt+ \epsilon dZ^{q,H}_t, X_0=x_0, 0\leq t \leq T$$…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…
This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1} w(x) f(x)$, where the weight function $w$ and the total weight $W=\int w(x) f(x) dx$ may not be known. The length-biased and…