Related papers: Minimax nonparametric testing in a problem related…
The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…
We consider a well defined joint detection and parameter estimation problem. By combining the Baysian formulation of the estimation subproblem with suitable constraints on the detection subproblem we develop optimum one- and two-step test…
Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The…
We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction -- the…
The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
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…
This paper addresses robust waveform design for multiple-input-multiple-output (MIMO) radar detection. A probabilistic model is proposed to describe the target uncertainty. Considering that waveform design based on maximizing the…
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…
We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold $M$, one wants to recover information about the geometry of $M$. Minimax estimators which have been proposed so far all…
Non Regression Testing (NRT) aims to check if software modifications result in undesired behaviour. Suppose the behaviour of the application previously known, this kind of test makes it possible to identify an eventual regression, a bug.…
The statistical characteristics of instance-label pairs often change with time in practical scenarios of supervised classification. Conventional learning techniques adapt to such concept drift accounting for a scalar rate of change by means…
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a…
In this paper, two types of linear estimators are considered for three related estimation problems involving set-theoretic uncertainty pertaining to $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ balls of frequency-responses. The problems at…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
A method for an evaluation of the error between an unknown parameter and its estimator is developed. Its application enables us to preserve the asymptotic power of a constructed test. Testing problems in AR(1) and ARCH models are studied…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of H\'{a}jek and Le Cam for classical statistical problems. We give complementary optimality results,…