TY - JOUR
T1 - Nonparametric estimation of location and scale parameters
AU - Potgieter, C.J.
AU - Lombard, F.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The first author's work was supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The second author's work was supported by the National Research Foundation of South Africa. The authors thank two referees for comments that led to an improved exposition of the work.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/12
Y1 - 2012/12
N2 - Two random variables X and Y belong to the same location-scale family if there are constants μ and σ such that Y and μ+σX have the same distribution. In this paper we consider non-parametric estimation of the parameters μ and σ under minimal assumptions regarding the form of the distribution functions of X and Y. We discuss an approach to the estimation problem that is based on asymptotic likelihood considerations. Our results enable us to provide a methodology that can be implemented easily and which yields estimators that are often near optimal when compared to fully parametric methods. We evaluate the performance of the estimators in a series of Monte Carlo simulations. © 2012 Elsevier B.V. All rights reserved.
AB - Two random variables X and Y belong to the same location-scale family if there are constants μ and σ such that Y and μ+σX have the same distribution. In this paper we consider non-parametric estimation of the parameters μ and σ under minimal assumptions regarding the form of the distribution functions of X and Y. We discuss an approach to the estimation problem that is based on asymptotic likelihood considerations. Our results enable us to provide a methodology that can be implemented easily and which yields estimators that are often near optimal when compared to fully parametric methods. We evaluate the performance of the estimators in a series of Monte Carlo simulations. © 2012 Elsevier B.V. All rights reserved.
UR - http://hdl.handle.net/10754/599000
UR - https://linkinghub.elsevier.com/retrieve/pii/S0167947312001478
UR - http://www.scopus.com/inward/record.url?scp=84864120616&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2012.03.021
DO - 10.1016/j.csda.2012.03.021
M3 - Article
SN - 0167-9473
VL - 56
SP - 4327
EP - 4337
JO - Computational Statistics & Data Analysis
JF - Computational Statistics & Data Analysis
IS - 12
ER -