Large deviations for method-of-quantiles estimators of one-dimensional parameters

Functional kernel estimators of large conditional quantiles

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...

Large Deviations for the One - Dimensional Edwards Model

ONE-DIMENSIONAL EDWARDS MODEL Mar h 6, 2002 Rem o van der Hofstad 1 2 Frank den Hollander 3 Wolfgang K onig 4 Abstra t: In this paper we prove a large deviation prin iple for the empiri al drift of a onedimensional Brownian motion with self-repellen e alled the Edwards model. Our results extend earlier work in whi h a law of large numbers, respe tively, a entral limit theorem were derived. In ...

2 Large Deviations for the One - Dimensional Edwards Model

In this paper we prove a large deviation principle for the empirical drift of a onedimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers, respectively, a central limit theorem were derived. In the Edwards model a path of length T receives a penalty eT , where HT is the self-intersection local time of the path a...

Quenched Large Deviations for One Dimensional Nonlinear Filtering

Consider the standard, one dimensional, nonlinear filtering problem for diffusion processes observed in small additive white noise: dXt = b(Xt)dt + dBt , dY ε t = γ(Xt)dt + εdVt , where B·, V· are standard independent Brownian motions. Denote by qε 1(·) the density of the law of Ξ1 conditioned on σ(Y ε t : 0 ≤ t ≤ 1). We provide “quenched” large deviation estimates for the random family of meas...