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Asymptotic distribution of regression correlation coefficient for Poisson regression model

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  • Takeshi Kurosawa
  • Nobuhiro Suzuki

Abstract

This study treats an asymptotic distribution for measures of predictive power for generalized linear models (GLMs). We focus on the regression correlation coefficient (RCC) that is one of the measures of predictive power. The RCC, proposed by Zheng and Agresti is a population value and a generalization of the population value for the coefficient of determination. Therefore, the RCC is easy to interpret and familiar. Recently, Takahashi and Kurosawa provided an explicit form of the RCC and proposed a new RCC estimator for a Poisson regression model. They also showed the validity of the new estimator compared with other estimators. This study discusses the new statistical properties of the RCC for the Poisson regression model. Furthermore, we show an asymptotic normality of the RCC estimator.

Suggested Citation

  • Takeshi Kurosawa & Nobuhiro Suzuki, 2018. "Asymptotic distribution of regression correlation coefficient for Poisson regression model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(1), pages 166-180, January.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:1:p:166-180
    DOI: 10.1080/03610926.2017.1300285
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    Cited by:

    1. Takeshi Kurosawa & Francis K.C. Hui & A.H. Welsh & Kousuke Shinmura & Nobuoki Eshima, 2020. "On goodness‐of‐fit measures for Poisson regression models," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 340-366, September.
    2. Minerva Mukhopadhyay & David B. Dunson, 2020. "Targeted Random Projection for Prediction From High-Dimensional Features," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1998-2010, December.

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