TITLE:
Robust Continuous Quadratic Distance Estimation Using Quantiles for Fitting Continuous Distributions
AUTHORS:
Andrew Luong
KEYWORDS:
Covariance Kernel, Influence Function, Hilbert Space, Linear Operator, GMM Estimation, Spectral Decomposition
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.4,
August
6,
2019
ABSTRACT: Quadratic
distance estimation making use of the sample quantile function over a
continuous range is introduced. It extends previous methods which are based
only on a few sample quantiles and it parallels the continuous GMM method.
Asymptotic properties are established for the continuous quadratic distance
estimators (CQDE) and the implementation of the methods are discussed. The
methods appear to be useful for balancing robustness and efficiency and useful
for fitting distribution with model quantile function being simpler than its
density function or distribution function.