Related papers: Optimal adaptive multidimensional-time signal ener…
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…
Optimal pointwise estimates are derived for the biharmonic Green function under Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal functions. A general upper bound for the nonasymptotic L_1-risk of the estimator is given. The method is applied to the shape respecting…
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A noise-uncertainty-free detector that is optimal in the low signal to noise ratio regime is analyzed in such a…
High-dimensional changepoint inference, adaptable to diverse alternative scenarios, has attracted significant attention in recent years. In this paper, we propose an adaptive and robust approach to changepoint testing. Specifically, by…
This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…
We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
Consider a target moving with a constant velocity on a unit-circumference circle, starting from an arbitrary location. To acquire the target, any region of the circle can be probed for its presence, but the associated measurement noise…
The paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic H\"older class estimator. Next applying…
We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated…
Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…