A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Representation theorem for convex nonparametric least squares
Tekijät: Kuosmanen T
Kustantaja: BLACKWELL PUBLISHING
Julkaisuvuosi: 2008
Journal: Econometrics Journal
Tietokannassa oleva lehden nimi: ECONOMETRICS JOURNAL
Lehden akronyymi: ECONOMET J
Vuosikerta: 11
Aloitussivu: 308
Lopetussivu: 325
Sivujen määrä: 18
ISSN: 1368-4221
DOI: https://doi.org/10.1111/j.1368-423X.2008.00239.x
Tiivistelmä
We examine a nonparametric least-squares regression model that endogenously selects the functional form of the regression function from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions can be characterized without a loss of generality by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrained to satisfy the required monotonicity and concavity conditions. This representation theorem is useful at least in three respects. First, it enables us to derive an explicit representation for the regression function, which can be used for assessing marginal properties and for the purposes of forecasting and ex post economic modelling. Second, it enables us to transform the infinite dimensional regression problem into a tractable quadratic programming (QP) form, which can be solved by standard QP algorithms and solver software. Importantly, the QP formulation applies to the general multiple regression setting. Third, an operational computational procedure enables us to apply bootstrap techniques to draw statistical inference.
We examine a nonparametric least-squares regression model that endogenously selects the functional form of the regression function from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions can be characterized without a loss of generality by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrained to satisfy the required monotonicity and concavity conditions. This representation theorem is useful at least in three respects. First, it enables us to derive an explicit representation for the regression function, which can be used for assessing marginal properties and for the purposes of forecasting and ex post economic modelling. Second, it enables us to transform the infinite dimensional regression problem into a tractable quadratic programming (QP) form, which can be solved by standard QP algorithms and solver software. Importantly, the QP formulation applies to the general multiple regression setting. Third, an operational computational procedure enables us to apply bootstrap techniques to draw statistical inference.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
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