Cramer-Rao Type Integral Inequalities for General Loss Functions
نویسنده
چکیده
Cramer-Rao type integral inequalities where developed for loss functions w(x) which are bounded below by functions of the type g(x) = c|x|l, l > 1. As applications, we obtain lower bounds of Hajek-LeCam type for locally asymptotic minimax error for such loss functions.
منابع مشابه
A generalized form of the Hermite-Hadamard-Fejer type inequalities involving fractional integral for co-ordinated convex functions
Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.
متن کاملSome Integral Inequalities of Hermite-Hadamard Type for Multiplicatively s-Preinvex Functions
In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.
متن کاملGeneral Hardy-Type Inequalities with Non-conjugate Exponents
We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
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 کاملNew Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications
Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.
متن کامل