期刊
IEEE ACCESS
卷 10, 期 -, 页码 14386-14396出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2022.3147231
关键词
Gamma distribution; Gamma regression; consistency and asymptotic normality; central limit theorem; maximum likelihood estimator
资金
- Fundamental Research Funds for the Central Universities of China [DUT21YG118]
- National Natural Science Foundation of China [U1560102, 61502074, 61633006]
This paper investigates the asymptotic properties of the maximum likelihood estimates of the Gamma distribution based generalized linear model (GaGLM). The score function and the Fisher information matrix for GaGLM are derived, and the asymptotic normality of the MLE is proven. Numerical results demonstrate the convergence of the MLE to a normal distribution.
The Gamma distribution based generalized linear model (GaGLM) is a kind of statistical model feasible for the positive value of a non-stationary stochastic system, in which the location and the scale are regressed by the corresponding explanatory variables. This paper theoretically investigates the asymptotic properties of maximum likelihood estimates (MLE) of GaGLM, which can benefit the further interval estimates, hypothesis tests and stochastic control design. First, the score function and the Fisher information matrix for GaGLM are derived. Then, the Lyapunov condition is derived to ensure the asymptotic normality of the score function normalized by the Fisher information matrix. Based on this condition, the asymptotic normality of the MLE of GaGLM is proven. Finally, a numerical example is given to testify the asymptotic properties obtained in the research. The numerical results indicate that the MLE of GaGLM converged to a normal distribution as the number of sample measurements increased.
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