AbstructWe consider the problem of estimating the order of a stationary ergodic Markov chain. Our focus is on estimators which satisfy a generalized Neyman-Pearson criterion of optimality. Specifically, the optimal estimator minimizes the probability of underestimation among all estimators with probability of overestimation not exceeding a given value. Our main result identifies the best expone...

Estimating distributions over large alphabets is a fundamental machine-learning tenet. Yet no method is known to estimate all distributions well. For example, add-constant estimators are nearly min-max optimal but often perform poorly in practice, and practical estimators such as absolute discounting, Jelinek-Mercer, and Good-Turing are not known to be near optimal for essentially any distribut...

This paper proposes the Fixed Effects Filtered (FEF) and Fixed Effects Filtered instrumental variable (FEF-IV) estimators for estimation and inference in the case of time-invariant effects in static panel data models when N is large and T is fixed. The FEF-IV allows for endogenous time-invariant regressors but assumes that there exists a suffi cient number of instruments for such regressors. It...

In a linear regression model with homoscedastic Normal noise, I consider James–Stein type shrinkage in the estimation of nuisance parameters associated with control variables. For at least three control variables and exogenous treatment, I show that the standard leastsquares estimator is dominated with respect to squared-error loss in the treatment effect even among unbiased estimators and even...

A general method of tail index estimation for heavy-tailed time series, based on examining the growth rate of the logged sample second moment of the data was proposed and studied in Meerschaert and Scheffler (1998) as well as Politis (2002). To improve upon the basic estimator, we introduce a scale-invariant estimator that is computed over subsets of the whole data set. We show that the new est...

This paper presents an a posteriori error estimator for the preconditioned iteration scheme of Bramble, Knyazev and Pasciak to compute the smallest eigenvalues together with its invariant subspace of an elliptic diierential operator. The error estimator is applied both to the nite element space in which the preconditioned iteration is performed (iteration error estimation) as well as to its hie...

As designers of artificial intelligence try to outwit hackers, both sides continue hone in on AI's inherent vulnerabilities. Designed and trained from certain statistical distributions data, deep neural networks (DNNs) remain vulnerable deceptive inputs that violate a DNN's statistical, predictive assumptions. Before being fed into network, however, most existing adversarial examples cannot mai...