The RKHS Approach to Minimum Variance Estimation Revisited: Variance Bounds, Sufficient Statistics, and Exponential Families
نویسندگان
چکیده
منابع مشابه
The Structure of Bhattacharyya Matrix in Natural Exponential Family and Its Role in Approximating the Variance of a Statistics
In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...
متن کاملOrdering of Order Statistics Using Variance Majorization
In this paper, we study stochastic comparisons of order statistics of independent random variables with proportional hazard rates, using the notion of variance majorization.
متن کاملNatural Exponential Families with Polynomial Variance Function and Umbral Calculus
In this paper we use the Umbral Calculus to investigate the relation between natural exponential families and Sheeer polynomials. We give a new proof for the classiication of univariate natural exponential families with quadratic variance function. We also show how our methods apply to natural exponential families with variance function of any order and to multivariate natural exponential famil...
متن کاملConjugate Priors for Exponential Families Having Cubic Variance Functions
In this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families (NEF’s). The first property says that the cumulant function of any basis of the family is a solution of some Monge-Ampère equation, the second is that the variance function satisfies a differential equation, and the third is characterized by the equality between two families...
متن کاملSMML estimators for exponential families with continuous sufficient statistics
The minimum message length principle is an information theoretic criterion that links data compression with statistical inference. This paper studies the strict minimum message length (SMML) estimator for d-dimensional exponential families with continuous sufficient statistics, for all d. The partition of an SMML estimator is shown to consist of convex polytopes (i.e. convex polygons when d = 2...
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 Transactions on Information Theory
سال: 2014
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2014.2317176