منابع مشابه
The Cramer-rao Inequality for Star Bodies
Associated with each body K in Euclidean n-space Rn is an ellipsoid 02K called the Legendre ellipsoid of K . It can be defined as the unique ellipsoid centered at the body’s center of mass such that the ellipsoid’s moment of inertia about any axis passing through the center of mass is the same as that of the body. In an earlier paper the authors showed that corresponding to each convex body K ⊂...
متن کاملImproved Cramer-Rao Inequality for Randomly Censored Data
As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...
متن کاملNote for Cramer-Rao Bounds
• (z)r and (z)i denote the real and imaginary part of z. II. CONSTRAINED CRAMER-RAO BOUND A. Problem Statement Problem statement and notation are based on [1]. • a: a K × 1 non-random vector which are to be estimated. • r: an observation of a random vector . • â (R): an estimate of a basing on the observed vector r . It is required that â (R) satisfies M nonlinear equality constraints (M < K), ...
متن کاملComputing Constrained Cramer Rao Bounds
We revisit the problem of computing submatrices of the Cramér-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter θ. We explore iterative methods that avoid direct inversion of the Fisher information matrix, which can be computationally expensive when the dimension of θ is large. The computation of the bound is related to the quadratic matrix program...
متن کاملGeometry of the Cramer-Rao bound
The Fisher information matrix determines how much information a measurement brings about the parameters that index the underlying probability distribution for the measurement. In this paper we assume that the parameters structure the mean value vector in a multivariate normal distribution. The Fisher matrix is. then a Gramian constructed from the sensitivity vectors that characterize the first-...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1977
ISSN: 0090-5364
DOI: 10.1214/aos/1176343754