Nonparametric quasi-likelihood
Nonparametric quasi-likelihood
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DOI：
10.1214/aos/1018031100
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发表时间：
1999-03
影响因子：
4.5
通讯作者：
Jeng-Min Chiou;H. Müller
中科院分区：
文献类型：
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作者：
Jeng-Min Chiou;H. Müller
韦德伯恩提出的拟似然函数通过指定方差函数而非整个分布，拓宽了广义线性模型的适用范围。然而，在拟似然方法中完全确定方差函数可能并不现实。我们通过用一个非参数方差函数估计值替代常规拟似然中的指定方差函数，定义了一种非参数拟似然。这个非参数方差函数估计值基于初始模型拟合的残差平方。推导了非参数方差函数估计量的收敛速度。结果表明，回归参数估计向量的渐近极限分布与在正确指定方差函数情况下得到的拟似然估计的渐近极限分布相同，从而确立了非参数拟似然估计的渐近有效性。我们基于偏差和皮尔逊卡方统计量提出了带宽选择策略。模拟结果表明，对于有限样本，所提出的非参数拟似然方法能够改进扩展拟似然或伪似然方法，在这些方法中，方差函数被假定属于具有未知参数的参数类。我们通过将所提出的方法应用于牙科数据和樱桃树数据进行了说明。
The quasi-likelihood function proposed by Wedderburn broadened the scope of generalized linear models by specifying the variance function instead of the entire distribution. However, complete specification of variance functions in the quasi-likelihood approach may not be realistic. We define a nonparametric quasi-likelihood by replacing the specified variance function in the conventional quasi-likelihood with a nonparametric variance function estimate. This nonparametric variance function estimate is based on squared residuals from an initial model fit. The rate of convergence of the nonparametric variance function estimator is derived. It is shown that the asymptotic limiting distribution of the vector of regression parameter estimates is the same as for the quasi-likelihood estimates obtained under correct specification of the variance function, thus establishing the asymptotic efficiency of the nonparametric quasi-likelihood estimates. We propose bandwidth selection strategies based on deviance and Pearson's chi-square statistic. It is demonstrated in simulations that for finite samples the proposed nonparametric quasi-likelihood method can improve upon extended quasi-likelihood or pseudo-likelihood methods where the variance function is assumed to fall into a parametric class with unknown parameters. We illustrate the proposed methods with applications to dental data and cherry tree data.