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Quantile Regression For Poisson Autoregressive Conditional Heteroskedasticity

Posted on:2017-04-21Degree:MasterType:Thesis
Country:ChinaCandidate:L ChangFull Text:PDF
GTID:2309330482495798Subject:Probability theory and mathematical statistics
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Since quantile regression was proposed in 1978, study about it has drawn great public attention. Of course, till today, its theory has been studied by many scholars. Compared with the traditional models, quantile regression can supply more information. It has more advantages than the least square estimation, describing statistical relationship among random variables more properly, and pay more attention to regressors impacting on the tail of response variable distribution. We reviewed previous studies of quantile regression that data types are from numeric data to qualitative data, and that variables are from continuous responses to discrete responses. In terms of choice of estimating methods, quantile regression model using a frequentist approach is very common, but it has many flaws for processing discrete data. A bayesian implementation is able to compensate for technical drawbacks because of traditional frequentist approach.In this article, we study the model of Poisson autoregressive conditional heteroskedasticity. We use quantile regression model in tradional frequentist method and in Bayesian method separately to estimate parameters of this model. At the same time, we study the asymptotic normality of estimated parameters and also show the proof of it. We give the expression of likelihood function in bayesian quantile regression. Although the posterior distribution is not available, MCMC methods will extract the posterior distribution. Furthermore, the differences between the estimated parameters of quantile regression in traditional frequentist method and in Bayesian method are compared through numerical simulation. The results verify that the Bayesian quantile method is the first choice for limited samples.
Keywords/Search Tags:Poisson autoregressive conditional heteroskedasticity, quantile regression, asymptotic normality, Bayesian quantile regression
PDF Full Text Request
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