## Hypothesis Testing

An obvious question is how to carry out various diagnostic tests done in the parametric econometrics within the nonparametric and semiparametric models. Several papers have appeared in the recent literature which deal with this issue. We present them here and show their links.

First consider the problem of testing a specified parametric model against a nonparametric alternative, H0 : /(p, x) = E(yi | xi) against H1 : m(x) = E(yi | xi). The idea behind the Ullah (1985) test statistic is to compare the parametric RSS (PRSS) XЙ2, x = Vi – /(S, xi) with the nonparametric RSS (NPRSS), XB2, where щ = – m(xi). His test statistic is

or simply T * = (PRSS – NPRSS), and reject the null hypothesis when T1 is large. л/П T1 has a degenerage distribution under H0...

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