Goodness-of-Fit Test Based on Smoothing Parameter Selection Criteria
Jong-Tae Kim
Abstract
Jong-Tae Kim
Abstract
The Proposed goodness-of-fit test Statistic derived from the test Statistc in Kim (1992) 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 in the event that is ejected. The limiting distribution of was obtained under the null hypothesis. It is also shown that this test is consistent against fixed alternatives.
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The Proposed goodness-of-fit test Statistic derived from the test Statistc in Kim (1992) 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 in the event that is ejected. The limiting distribution of was obtained under the null hypothesis. It is also shown that this test is consistent against fixed alternatives.
Key concepts: Goodness of fit, Test statistic, Mathematics, Statistics, Estimator, Smoothing, Anderson–Darling test, Statistic