Asymptotic Theory of Statistical Estimation 1 Jiantao Jiao

Beyond Maximum Likelihood: from Theory to Practice

Maximum likelihood is the most widely used statistical estimation technique. Recent work by Jiao, Venkat, Han, and Weissman [1] introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements both in theory and in practice over the maximum likelihood estimator (MLE), particularly in high dimensional scenarios involving para...

Minimax Estimation of Discrete Distributions under $\ell_1$ Loss

We consider the problem of discrete distribution estimation under l1 loss. We provide tight upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in regimes where the support size S may grow with the number of observations n. We show that among distributions with bounded entropy H , the asymptotic maximum risk for the e...

Lecture 12 : Minimax Decision Theory and Asymptotics

Minimax estimation of the L1 distance

We consider the problem of estimating the L1 distance between two discrete probability measures P and Q from empirical data in a nonasymptotic and large alphabet setting. When Q is known and one obtains n samples from P , we show that for every Q, the minimax rate-optimal estimator with n samples achieves performance comparable to that of the maximum likelihood estimator (MLE) with n lnn sample...

Estimation in ARMA models based on signed ranks

In this paper we develop an asymptotic theory for estimation based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and we illustrate the performa...