Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications
نویسندگان
چکیده
منابع مشابه
Error Bounds in Parameter Estimation Under Mismatch
In this paper we develop a new upper bound for the mean square estimation error of a parameter that takes values on a bounded interval. The bound is based on the discretization of the region into a finite number of points, and the determination of the estimate by a maximum likelihood procedure. It is assumed that inaccurate versions of the true spectra are utilized in the implementation of the ...
متن کاملMean Square Error bounds for parameter estimation under model misspecification
In parameter estimation, assumptions about the model are typically considered which allow us to build optimal estimation methods under many statistical senses. However, it is usually the case where such models are inaccurately known or not capturing the complexity of the observed phenomenon. A natural question arises to whether we can find fundamental estimation bounds under model mismatches. T...
متن کاملGeometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints
We consider parameter estimation in distributed networks, where each node in the network observes an independent sample from an underlying distribution and has k bits to communicate its sample to a centralized processor which computes an estimate of a desired parameter of the distribution. We develop lower bounds for the minimax risk of estimating the underlying parameter under squared l2 loss ...
متن کاملAgnostic Estimation for Misspecified Phase Retrieval Models
The goal of noisy high-dimensional phase retrieval is to estimate an s-sparse parameter β∗ ∈ R from n realizations of the model Y = (X>β∗)2 + ε. Based on this model, we propose a significant semi-parametric generalization called misspecified phase retrieval (MPR), in which Y = f(X>β∗, ε) with unknown f and Cov(Y, (X>β∗)2) > 0. For example, MPR encompasses Y = h(|X>β∗|) + ε with increasing h as ...
متن کاملEfficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models
It has been shown that AIC-type criteria are asymptotically efficient selectors of the tuning parameter in non-concave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regres...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Signal Processing Magazine
سال: 2017
ISSN: 1053-5888
DOI: 10.1109/msp.2017.2738017