X2 goodness-of-fit tests for polynomial regression
Titel:
X2 goodness-of-fit tests for polynomial regression
Auteur:
Novo, L. A. Ramil Manteiga, W. Gonzalez
Verschenen in:
Communications in statistics
Paginering:
Jaargang 27 (1998) nr. 1 pagina's 229-258
Jaar:
1998
Inhoud:
In the context of nonparametric regression models, we propose a very general procedure to test the goodness-of-fit of the regression function underlying in a set of (xi,yi) data, to a polynomial type family of regression curves. Test statistics are based on residual sums of squares obtained by a comparison of a nonparametric fit, HY, versus a parametric fit, PY, via RSS(HY,PY)=(HY - PY)T(HY - PY) or versus a smoothed parametric fit, via RSS(HY,HPY)=(HY - HPY)T(HY - HPY). A X2 distribution with degrees of freedom determined by the hat matrixes H and P is used to approximate the distribution of test statistics. The proposed procedure generalizes classical least squares theory and involves a variety of different nonparametric smoothing techniques. A comparison among X2 tests with different smoothing techniques and with previous procedures based on a normal distribution and bootstrap is made by means of a simulation study.
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