Related papers: On asymptotically efficient statistical inference …
This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymptotic formulas for the mean square errors of the filtering…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a computationally simple, sample eigenvalue based procedure for estimating the number of…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simplex conjecture". We discuss possible approaches to it, and…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…
We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate…
We consider the problem of estimating the proportion $\theta$ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…