Related papers: Minimax asymptotics
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We present a new and relatively elementary method for studying the solution of the initial-value problem for dispersive linear and integrable equations in the large-$t$ limit, based on a generalization of steepest descent techniques for…
Consider the problem of sampling sequentially from a finite number of $N \geq 2$ populations, specified by random variables $X^i_k$, $ i = 1,\ldots , N,$ and $k = 1, 2, \ldots$; where $X^i_k$ denotes the outcome from population $i$ the…
The method of optimizing entropy is used to (i) conduct Asymptotic Hypothesis Testing and (ii) determine the particle distribution for which Entropy is maximized. This paper focuses on two related applications of Information Theory:…
In this paper, we propose an estimator of the generalized maximum mean discrepancy between several distributions, constructed by modifying a naive estimator. Asymptotic normality is obtained for this estimator both under equality of these…
Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the…
In this paper we deal with the regression problem in a random design setting. We investigate asymptotic optimality under minimax point of view of various Bayesian rules based on warped wavelets and show that they nearly attain optimal…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
We study asymptotically minimax predictive distributions in an infinite sequence model. First, we discuss the connection between the prediction in the infinite sequence model and the prediction in the function model. Second, we construct an…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…