Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

On Cluster Regression and Factor Analysis Models with Elliptic t Errors

Brajendra C. Sutradhar
Lecture Notes-Monograph Series
Vol. 24, Multivariate Analysis and Its Applications (1994), pp. 369-383
Stable URL: http://www.jstor.org/stable/4355817
Page Count: 15
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Cluster Regression and Factor Analysis Models with Elliptic t Errors
Preview not available

Abstract

This paper deals with a two-stage cluster sampling problem. At the first stage k clusters are drawn at random, and then at the second stage n p-dimensional correlated observations are chosen under each cluster, which may be linearly related to certain covariates. The data of this type can be represented by a cluster regression model with suitable distributional assumption for the errors. In this paper, it is assumed that the error vector of the linear model follow an np-dimensional elliptically contoured t-distribution. Many elliptical distribution theory results are developed in the literature under the assumption that these n p-dimensional errors are uncorrelated. But, in the case of cluster sampling, errors are usually assumed to be equicorrelated. We, therefore, introduce a suitable np × np covariance matrix for n p-dimensional errors which takes the common intra-cluster correlation into account. We then study the likelihood inferences for the regression parameters (coefficients of the covariates) of the (linear) cluster regression model. Maximum likelihood estimators (m.l.e.) of the regression parameters are found to be more efficient than the generalized least squares estimators for smaller values of the degrees of freedom parameter of the elliptically contoured t-distribution. The asymptotic (k → ∞) distribution of the m.l.e. of the regression coefficients is also given. Further, a factor analysis model is studied. Based on the assumption that n p-dimensional observations are uncorrelated and they follow np-dimensional elliptically contoured t-distribution, we have developed Neyman's partial score test for testing the suitability of the number of factors. The test statistic has asymptotically χ 2 distribution with suitable degrees of freedom. Moreover, the test is asymptotically optimal.

Page Thumbnails

  • Thumbnail: Page 
[369]
    [369]
  • Thumbnail: Page 
370
    370
  • Thumbnail: Page 
371
    371
  • Thumbnail: Page 
372
    372
  • Thumbnail: Page 
373
    373
  • Thumbnail: Page 
374
    374
  • Thumbnail: Page 
375
    375
  • Thumbnail: Page 
376
    376
  • Thumbnail: Page 
377
    377
  • Thumbnail: Page 
378
    378
  • Thumbnail: Page 
379
    379
  • Thumbnail: Page 
380
    380
  • Thumbnail: Page 
381
    381
  • Thumbnail: Page 
382
    382
  • Thumbnail: Page 
383
    383