Related papers: Statistical estimation requires unbounded memory
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Any repeated use of a fixed experimental instrument is subject to memory effects. We design an estimation method uncovering the details of the underlying interaction between the system and the internal memory without having any experimental…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
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…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the…
This study proposes a robust estimator for stochastic frontier models by integrating the idea of Basu et al. [1998, Biometrika 85, 549-559] into such models. We verify that the suggested estimator is strongly consistent and asymptotic…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…