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Conditional Distribution Model Specification Testing Using Chi-Square Goodness-of-Fit Tests

Author

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  • Delgado, M. A.
  • Vainora, J.

Abstract

This paper introduces chi-square goodness-of-fit tests to check for conditional distribution model specification. The data is cross-classified according to the Rosenblatt transform of the dependent variable and the explanatory variables, resulting in a contingency table with expected joint frequencies equal to the product of the row and column marginals, which are independent of the model parameters. The test statistics assess whether the difference between observed and expected frequencies is due to chance. We propose three types of test statistics: the classical trinity of tests based on the likelihood of grouped data, and two statistics based on the efficient raw data estimator-namely, a Chernoff-Lehmann and a generalized Wald statistic. The asymptotic distribution of these statistics is invariant to sample-dependent partitions. Monte Carlo experiments demonstrate the good performance of the proposed tests.

Suggested Citation

  • Delgado, M. A. & Vainora, J., 2024. "Conditional Distribution Model Specification Testing Using Chi-Square Goodness-of-Fit Tests," Cambridge Working Papers in Economics 2440, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2440
    Note: jv429
    as

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    File URL: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe2440.pdf
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    References listed on IDEAS

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    1. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(3), pages 348-358, June.
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    More about this item

    Keywords

    Conditional Distribution Specification Testing; Rosenblatt Transform; Pearson Statistic; Trinity of Chi-Square Tests; Generalized Wald Statistic;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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