Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

Notions of Limiting P Values Based on Data Depth and Bootstrap

Regina Y. Liu and Kesar Singh
Journal of the American Statistical Association
Vol. 92, No. 437 (Mar., 1997), pp. 266-277
DOI: 10.2307/2291471
Stable URL: http://www.jstor.org/stable/2291471
Page Count: 12
  • Download ($14.00)
  • Cite this Item
Notions of Limiting P Values Based on Data Depth and Bootstrap
Preview not available

Abstract

In this article we propose some new notions of limiting P values for hypothesis testing. The limiting P value (LP) here not only provides the usual attractive interpretation of a P value as the strength in support of the null hypothesis coming from the observed data, but also has several advantages. First, it allows us to resample directly from the empirical distribution (in the bootstrap implementations), rather than from the estimated population distribution satisfying the null constraints. Second, it serves as a test statistic and as a P value simultaneously, and thus enables us to obtain test results directly without having to construct an explicit test statistic and then establish or approximate its sampling distribution. These are the two steps generally required in a standard testing procedure. Using bootstrap and the concept of data depth, we have provided LP's for a broad class of testing problems where the parameters of interest can be either finite or infinite dimensional. Some computer simulation results show the generality and the computational feasibility of our approach.

Page Thumbnails

  • Thumbnail: Page 
266
    266
  • Thumbnail: Page 
267
    267
  • Thumbnail: Page 
268
    268
  • Thumbnail: Page 
269
    269
  • Thumbnail: Page 
270
    270
  • Thumbnail: Page 
271
    271
  • Thumbnail: Page 
272
    272
  • Thumbnail: Page 
273
    273
  • Thumbnail: Page 
274
    274
  • Thumbnail: Page 
275
    275
  • Thumbnail: Page 
276
    276
  • Thumbnail: Page 
277
    277