SCIRP Mobile Website
Paper Submission

Why Us? >>

  • - Open Access
  • - Peer-reviewed
  • - Rapid publication
  • - Lifetime hosting
  • - Free indexing service
  • - Free promotion service
  • - More citations
  • - Search engine friendly

Free SCIRP Newsletters>>

Add your e-mail address to receive free newsletters from SCIRP.

 

Contact Us >>

WhatsApp  +86 18163351462(WhatsApp)
   
Paper Publishing WeChat
Book Publishing WeChat
(or Email:book@scirp.org)

Article citations

More>>

Sethuraman and Rao, J.S. (1970) Pitman Efficiencies of Tests Based on Spacings in Nonparametric Techniques in Statistical Inference. Puri, M.L., Ed. Cambridge University Press, Cambridge.

has been cited by the following article:

  • TITLE: Asymptotic Results for Goodness-of-Fit Tests Using a Class of Generalized Spacing Methods with Estimated Parameters

    AUTHORS: Andrew Luong

    KEYWORDS: Density Based Tests, EDF Tests, Anderson-Darling Statistic, Hellinger Distance Statistic, Pseudo-Distance, Maximum Spacing Method

    JOURNAL NAME: Open Journal of Statistics, Vol.8 No.4, August 27, 2018

    ABSTRACT: A class of pseudo distances is used to derive test statistics using transformed data or spacings for testing goodness-of-fit for parametric models. These statistics can be considered as density based statistics and expressible as simple functions of spacings. It is known that when the null hypothesis is simple, the statistics follow asymptotic normal distributions without unknown parameters. In this paper we emphasize results for the null composite hypothesis: the parameters can be estimated by a generalized spacing method (GSP) first which is equivalent to minimize a pseudo distance from the class which is considered; subsequently the estimated parameters are used to replace the parameters in the pseudo distance used for estimation; goodness-of-fit statistics for the composite hypothesis can be constructed and shown to have again an asymptotic normal distribution without unknown parameters. Since these statistics are related to a discrepancy measure, these tests can be shown to be consistent in general. Furthermore, due to the simplicity of these statistics and they come a no extra cost after fitting the model, they can be considered as alternative statistics to chi-square statistics which require a choice of intervals and statistics based on empirical distribution (EDF) using the original data with a complicated null distribution which might depend on the parametric family being considered and also might depend on the vector of true parameters but EDF tests might be more powerful against some specific models which are specified by the alternative hypothesis.