Spline-based quasi-likelihood estimation of mixed Poisson regression with single-index models (Q683863)

This article proposes a quasi-likelihood estimation approach for mixed Poisson regression with single-index models. The unknown smooth function is approximated by a linear combination of B-spline basis functions, and a modified Fisher scoring algorithm is employed to compute the estimates. The method takes into account the bias due to the spline approximation, and the spline estimators can achieve the optimal rate of convergence by allowing the sample size increasing at an appropriate rate. A consistent estimation method of the asymptotic variance of the regression parameter estimates can be derived by exploiting the spline approximation. Semiparametric efficiency for the regression parameters estimators is established. The finite sample performance of the proposed method is evaluated by Monte Carlo simulation. A data set from an air pollution study was analyzed to illustrate the proposed method.