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The distribution of Pearson residuals in generalized linear models

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  • Cordeiro, Gauss M.
  • Simas, Alexandre B.

Abstract

In general, the distribution of residuals cannot be obtained explicitly. In this paper we give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order n-1, where n is the sample size. We define a set of corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. An application to a real data set and simulation results for a gamma model illustrate the usefulness of our corrected Pearson residuals.

Suggested Citation

  • Cordeiro, Gauss M. & Simas, Alexandre B., 2009. "The distribution of Pearson residuals in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3397-3411, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3397-3411
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    References listed on IDEAS

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    1. D. A. Williams, 1987. "Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 181-191, June.
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    2. Leslie Chandrakantha, 2019. "Risk Prediction Model for Dengue Transmission Based on Climate Data: Logistic Regression Approach," Stats, MDPI, vol. 2(2), pages 1-12, May.
    3. R. S. Sparks & T. Keighley & D. Muscatello, 2011. "Optimal exponentially weighted moving average (EWMA) plans for detecting seasonal epidemics when faced with non-homogeneous negative binomial counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2165-2181.
    4. Wu, K.Y.K. & Li, W.K., 2016. "On a dispersion model with Pearson residual responses," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 17-27.
    5. Boris Aleksandrov & Christian H. Weiß, 2020. "Testing the dispersion structure of count time series using Pearson residuals," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 325-361, September.

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