Related papers: Minimax-robust estimation problems for sequences w…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…
We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…
Estimation of the mean and covariance functions is a fundamental problem in functional data analysis, particularly for discretely observed functional data. In this work, we study a regularization-based framework for estimating the mean and…
We consider minimax signal detection in the sequence model. Working with certain ellipsoids in the space of square-summable sequences of real numbers, with a ball of positive radius removed, we obtain upper and lower bounds for the minimax…
The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter of…
Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
This paper studies the problem of fault detection and estimation (FDE) for linear time-invariant (LTI) systems with a particular focus on frequency content information of faults, possibly as multiple disjoint continuum ranges, and under…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…
This paper addresses the problem of estimating multiplicative fault signals in linear time-invariant systems by processing its input and output variables, as well as designing an input signal to maximize the accuracy of such estimates. The…
A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…
In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, "$N$-convex functionals" (the simplest example being the maximum of several fractional-linear functions) of unknown "signal"…
We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new…
The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However,…
In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…