On Assessing Goodness of Fit of Generalized Linear Models to Sparse Data
针对非标准广义线性模型，改进了Pearson统计量，使其与回归参数局部正交，从而简化计算并提高检验稀疏数据拟合优度的功效。
SUMMARY Approximations to the first three moments of Pearson's statistic are obtained for non-canonical generalized linear models, extending the results of McCullagh. A first-order modification to Pearson's statistic is proposed which induces local orthogonality with the regression parameters, resulting in substantial simplifications and increased power. Accurate and easily computed approximations to the moments of the modified Pearson statistic conditional on the estimated regression parameters are obtained for testing goodness of fit to sparse data. Both the Pearson statistic and its modification are shown to be asymptotically independent of the regression parameters. Simulation studies and examples are given.