The X2-goodness-of-fit tests with moment type estimators |
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Authors: | A Hsuan D S Robson |
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Institution: | 1. University of Delaware , Newark, Delaware, 19711;2. Cornell University , Ithaca, N.Y, 14850 |
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Abstract: | In the x2-goodness-of-fit test the underlying null hypothesis usually involves unknown parameters. In this article we study the asymptotic distribution of the Pearson statistic when the unknown parameters are estimated by a moment type estimator based on the ungrouped data. As is expected the usual Pearson statistic is no longer asymptotically x2-distributed in this situation. We propose a statistic Qcirc] which under certain regularity conditions is asymptotically x2-distributed. We also propose a statistic Q? for the goodness-of-fit test when the class boundaries are random. The asymptotic powers of Qcirc] and Qcirc]? tests are discussed. |
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Keywords: | ungrouped data random cells asymptotic distributions |
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