Delta method in large deviations and moderate deviations for estimators
نویسندگان
چکیده
منابع مشابه
Delta Method in Large Deviations and Moderate Deviations for Estimators by Fuqing
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large devi...
متن کاملLarge and moderate deviations principles for kernel estimators of the multivariate regression
Abstract : In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the unidimensional case for the Nadaraya-Watson estimator. Moreover, we giv...
متن کاملFunctional Large Deviations and Moderate Deviations for Markov-modulated Risk Models with Reinsurance
We establish a functional large deviation principle and a functional moderate deviation principle for Markov-modulated risk models with reinsurance by constructing an exponential martingale approach. Lundberg’s estimate of the ruin time is also presented.
متن کاملModerate Deviations of Maximum Likelihood Estimators under Alternatives
Since statistical models are simplifications of reality, it is important in estimation theory to study the behavior of estimators also under distributions (slightly) different from the proposed model. In testing theory, when dealing with test statistics where nuisance parameters are estimated, knowledge of the behavior of the estimators of the nuisance parameters is needed under alternatives to...
متن کاملLarge and moderate deviations for matching problems and empirical discrepancies
We study the two-sample matching problem and its connections with the Monge-Kantorovich problem of optimal transportation of mass. We exploit this connection to obtain moderate and large deviation principles. For the classical problem on the unit square we present a conjecture which, if true, yields an explicit formula for the rate function.
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: The Annals of Statistics
سال: 2011
ISSN: 0090-5364
DOI: 10.1214/10-aos865