The estimator in poisson regression model equal zero when it is used maximum likelihood method to estimate the parameter of the model which is mention above , what is the method is used to get the parameter?
First, have a look at the plots (particularly scatterplots) to see whether your data meet the presumptions of the Poisson regression model or not. The non-significance of the coefficients indicates that the selected model is not what you are looking for; It does not suit the data under study. However, the least-square error is another criterion you can apply.
Read up on poisson regression and how to estimate its parameters. ML is not usually used. Suggest you see Lachin, Biostatistical Methods 2nd.ed. on this topic. It's authoritative. Best wishes, David Booth
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