# zbMATH — the first resource for mathematics

Goodness-of-fit test for linear models based on local polynomials. (English) Zbl 0946.62016
Summary: We test if a regression function belongs to a class of parametric models by measuring the discrepancy between a parametric fit and a local polynomial regression. The proposed test is a weighted $$L^2$$-norm of a smoothed function based on the parametric residuals.

##### MSC:
 62F03 Parametric hypothesis testing 62G08 Nonparametric regression and quantile regression 62G09 Nonparametric statistical resampling methods 62G10 Nonparametric hypothesis testing
##### Keywords:
model checking; bootstrap; local polynomial
Full Text:
##### References:
 [1] de Jong, P., A central limit theorem for generalized quadratic forms, Probab. theory related fields, 75, 261-277, (1987) · Zbl 0596.60022 [2] Eubank, R.; Hart, J., Testing goodness-of-fit in regression via order selection criteria, Ann. statist., 20, 1412-1425, (1992) · Zbl 0776.62045 [3] Fan, J., Gijbels, I., 1996. Local Polynomial Modeling and its Applications, Chapman&Hall, New York. · Zbl 0873.62037 [4] Härdle, W.; Mammen, E., Comparing nonparametric versus parametric regression fits, Ann. statist., 21, 1926-1947, (1993) · Zbl 0795.62036 [5] Stute, W., 1997. Nonparametric model checks for regression. Ann. Statist. 25, 613-641. · Zbl 0926.62035 [6] Stute, W.; González-Manteiga, W., NN goodness-of-fit test for linear models, J. statist. plann. inference, 53, 75-92, (1996) · Zbl 0847.62036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.