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Goodness of fit and related inference processes for quantile regression. (English) Zbl 0998.62041
Summary: We introduce a goodness-of-fit process for quantile regression analogous to the conventional \(R^2\) statistic of least squares regression. Several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated. The asymptotic behavior of the inference processes is shown to be closely related to earlier \(p\)-sample goodness-of-fit theory involving Bessel processes. The approach is illustrated with some hypothetical examples, an application to recent empirical models of international economic growth, and some Monte Carlo evidence.

62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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