Goodness-of-Fit Test Based on Smoothing Parameter Selection Criteria

  • Published : 1995.04.01


The objective of this research is to investigate the problem of goodness-of-fit testing based on nonparametric density estimation with a data-driven smoothing parameter. The small and large sample properties of a new test statistic $\hat{\lambda_a}$ is investigated. The test statistic $\hat{\lambda_a}$ is itself a smoothing parameter which is selected to minimize an estimated MISE for a truncated series estimator of the comparison density function. Therefore, this test statistic leads immediately to a point estimate of the density function th the event that $H_0$ is rejected. The limiting distribution of $\hat{\lambda_a}$ is obtained under the null hypothesis. It is also shown that this test is consistent against fixed alternatives.



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