Related papers: Minimax asymptotics
The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators…
Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…
The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely understood. This paper studies the superiority of symplectic…
Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
We consider a general problem of finding a strategy that minimizes the exponential moment of a given cost function, with an emphasis on its relation to the more common criterion of minimization the expectation of the first moment of the…
Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called $M$-estimands, and can be estimated by $M$-estimators -- minimizers of empirical average…
Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an…
We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the…
This paper reviews recent developments in fundamental limits and optimal algorithms for change point analysis. We focus on minimax optimal rates in change point detection and localisation, in both parametric and nonparametric models. We…
The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…