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A property of projection residuals with applications to concave regression

Author

Listed:
  • Kuhlmann, Dietrich W.
  • Wright, F. T.

Abstract

The residuals of the l-2-projection onto a linear subspace, or more generally onto a closed, convex cone, which contains the constant vectors sum to zero, i.e. if y* is the projection of y, then y1 - y1* + tdot + y2 - y2* + ... + yn* = 0. The analogue of this result for least absolute deviations, as well as for other objective functions, is established. The application of these results in establishing the consistency of the l1 and l2 estimates of concave regression functions is discussed.

Suggested Citation

  • Kuhlmann, Dietrich W. & Wright, F. T., 1993. "A property of projection residuals with applications to concave regression," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 313-319, March.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:4:p:313-319
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