Minimum distance tests and estimates based on ranks

NAVRÁTIL, Radim. Minimum distance tests and estimates based on ranks. REVSTAT Statistical Journal. Lisabon: Statistics Portugal, 2020, vol. 18, No 3, p. 299-310. ISSN 1645-6726.

Basic information

• Original name: Minimum distance tests and estimates based on ranks
• Authors: NAVRÁTIL, Radim (203 Czech Republic, guarantor, belonging to the institution).
• Edition: REVSTAT Statistical Journal, Lisabon, Statistics Portugal, 2020, 1645-6726.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10103 Statistics and probability
• Country of publisher: Portugal
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 1.250
• RIV identification code: RIV/00216224:14310/20:00117545
• Organization unit: Faculty of Science
• UT WoS: 000557809200004
• Keywords in English: minimum distance estimates; ranks; robustness; tests.
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

It is well known that the least squares estimate in classical linear regression model is very sensitive to violation of the assumptions, in particular normality of model errors. That is why a lot of alternative estimates has been developed to overcome these shortcomings. Quite interesting class of such estimates is formed by R-estimates. They use only ranks of response variable instead of their actual value. The goal of this paper is to extend this class by another estimates and tests based only on ranks. First, we will introduce a new rank test in linear regression model. The test statistic is based on a certain minimum distance estimator, but unlike classical rank tests in regression it is not a simple linear rank statistic. Then, we will return back to estimates and generalize minimum distance estimates for various type of distances. We will show that in some situation these tests and estimates have greater power than the classical ones. Theoretical results will be accompanied by a simulation study to illustrate finite sample behavior of estimates and tests.

Links

• MUNI/A/1204/2017, interní kód MU: Name: Matematické statistické modelování 2 (Acronym: MaStaMo2)

Investor: Masaryk University, Category A