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Testing distributional assumptions using a continuum of moments. (English) Zbl 1464.62223

Summary: We propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test, which takes into account the correlation between influence functions for different argument values. We derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size. We show its consistency against any deviation from the null, study its local power and compare it with existing tests. An extensive Monte Carlo exercise confirms that our proposed tests display good power in finite samples against a variety of alternatives.

MSC:

62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62F05 Asymptotic properties of parametric tests
62P20 Applications of statistics to economics
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