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 SEGMENTED MULTIVARIATE REGRESSION

Jian Liu, Shiying Wu and James V. Zidek
Statistica Sinica
Vol. 7, No. 2 (April 1997), pp. 497-525
Stable URL: http://www.jstor.org/stable/24306090
Page Count: 29
  • Read Online (Free)
  • 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 SEGMENTED MULTIVARIATE REGRESSION
Preview not available

Abstract

This paper concerns segmented multivariate regression models, models which have different linear forms in different subdomains of the domain of an independent variable. Without knowing that number and their boundaries, we first estimate the number of these subdomains using a modified Schwarz criterion. The estimated number of regions proves to be weakly consistent under fairly general conditions. We then estimate the subdomain boundaries ("thresholds") and the regression coefficients within subdomains by minimizing the sum of squares of the residuals. We show that the threshold estimates converge (at rates, 1/n and n−1/2, respectively at the model's threshold points of discontinuity and continuity) and that the regression coefficients as well as the residual variances are asymptotically normal. The basic condition on the error distribution required for the veracity of our asymptotic results is satisfied by any distribution with zero mean and a moment generating function (having bounded second derivative around zero). As an illustration, a segmented bivariate regression model is fitted to real data and the relevance of the asymptotic results is examined via simulations.

Page Thumbnails

  • Thumbnail: Page 
[497]
    [497]
  • Thumbnail: Page 
498
    498
  • Thumbnail: Page 
499
    499
  • Thumbnail: Page 
500
    500
  • Thumbnail: Page 
501
    501
  • Thumbnail: Page 
502
    502
  • Thumbnail: Page 
503
    503
  • Thumbnail: Page 
504
    504
  • Thumbnail: Page 
505
    505
  • Thumbnail: Page 
506
    506
  • Thumbnail: Page 
507
    507
  • Thumbnail: Page 
508
    508
  • Thumbnail: Page 
509
    509
  • Thumbnail: Page 
510
    510
  • Thumbnail: Page 
511
    511
  • Thumbnail: Page 
512
    512
  • Thumbnail: Page 
513
    513
  • Thumbnail: Page 
514
    514
  • Thumbnail: Page 
515
    515
  • Thumbnail: Page 
516
    516
  • Thumbnail: Page 
517
    517
  • Thumbnail: Page 
518
    518
  • Thumbnail: Page 
519
    519
  • Thumbnail: Page 
520
    520
  • Thumbnail: Page 
521
    521
  • Thumbnail: Page 
522
    522
  • Thumbnail: Page 
523
    523
  • Thumbnail: Page 
524
    524
  • Thumbnail: Page 
525
    525