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We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
We analyze the Allan Variance estimator as the combination of Discrete-Time linear filters. We apply this analysis to the different variants of the Allan variance: the Overlapping Allan Variance, the Modified Allan variance, the Hadamard…
The time series with periodic behavior, such as the periodic autoregressive (PAR) models belonging to the class of the periodically correlated processes, are present in various real applications. In the literature, such processes were…
In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…
In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise…
This paper is concerned with model averaging estimation for partially linear functional score models. These models predict a scalar response using both parametric effect of scalar predictors and non-parametric effect of a functional…
This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…
We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many…
The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability…
Robust adaptation of LLMs and VLMs is often evaluated by average accuracy or average consistency under perturbations. However, these averages can hide a structured failure mode: a prediction may remain correct while probability mass already…
The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression…
In this work, time series analysis techniques are used to analyze sequential, equispaced mass measurements of a Si density artifact, collected from an electromechanical transducer. Specifically, techniques such as Power Spectral Density,…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…