Meta-Bound on Lower Bounds of Bayes Risk in Parameter Estimation

نویسندگان

چکیده

Information-theoretic lower bounds of the Bayes risk have been investigated for a problem parameter estimation in Bayesian setting. Previous studies proven bound different manner and characterized via quantities such as mutual information, Sibson's α-mutual f-divergence, Csiszár's f-informativity. In this paper, we introduce an inequality called “meta-bound risk” show that previous results can be derived from inequality.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Bayes Risk Lower Bounds

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound on the minimax risk, but also characterizes the fundamental limit of any estimator given the prior knowledge. Our bounds are based on the notion of f -inform...

متن کامل

Lower Bounds for Bayes Error Estimation

ÐWe give a short proof of the following result. Let …X; Y † be any distribution on N f0; 1g, and let …X1; Y1†; . . . ; …Xn; Yn† be an i.i.d. sample drawn from this distribution. In discrimination, the Bayes error L ˆ infg Pfg…X† 6ˆ Y g is of crucial importance. Here we show that without further conditions on the distribution of …X; Y †, no rate-of-convergence results can be obtained. Let n…X1; ...

متن کامل

Bounds on the Bayes and minimax risk for signal parameter estimation

A 3 r m h estimating the parameter 0 from a parametrized signal problem (with 0 5 0 5 L) observed through Gaussian white noise, four useful and computable lower bounds for the Bayes risk were developed. For problems with different L and Merent signal to noise ratios, some bounds am superior to the others. The lower bound obtained from taking the maximum of the four, serves not only as a good lo...

متن کامل

Geometric 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 کامل

Extended Ziv-Zakai lower bound for vector parameter estimation

The Bayesian Ziv–Zakai bound on the mean square error (MSE) in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than MSE. The extended bound is evaluated for some representative problems in time-delay and bearing estimation. The resulting bounds have simple closed-form expressions, ...

متن کامل

ذخیره 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: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

سال: 2023

ISSN: ['1745-1337', '0916-8508']

DOI: https://doi.org/10.1587/transfun.2023tap0002