Parameterization and inference for nonparametric regression problems
Parameterization and inference for nonparametric regression problems
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DOI：
10.1111/1467-9868.00300
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发表时间：
2001-01-01
影响因子：
5.8
通讯作者：
Carroll, RJ
中科院分区：
文献类型：
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作者：
Jiang, WX;Kipnis, V;Carroll, RJ
我们考虑局部似然或局部估计方程，其中估计了多元函数Theta(.)，但感兴趣的是Theta（.）的派生函数lambda（.）。在许多应用中，最自然的推导函数是Theta（.）的非线性函数。在试图理解导出的非线性函数是常数还是线性时，这种方法会出现一个问题：当函数实际上是常数或线性时，函数估计的期望不必是常数或线性，至少到二阶。在这种情况下，非参数回归中用于检验函数是常数还是线性的最简单的标准方法不能应用。我们给出了一个简单的通解，它适用于非参数回归、变系数模型、非参数广义线性模型等。我们证明，在局部线性核回归中，关于衍生函数lambda（.）的推断是容易的，而不需要通过重新参数化来损失功率，因此lambda（.）本身是Theta（.）的一个分量。我们的方法与为了方便而选择Theta（.）并允许lambda（.）是Theta（.）的非线性函数的标准做法相反。该方法应用于营养流行病学的一个重要数据集。
We consider local likelihood or local estimating equations, in which a multivariate function Theta(.) is estimated but a derived function lambda(.) of Theta(.) is of interest. In many applications, when most naturally formulated the derived function is a non-linear function of Theta(.). In trying to understand whether the derived non-linear function is constant or linear, a problem arises with this approach: when the function is actually constant or linear, the expectation of the function estimate need not be constant or linear, at least to second order. In such circumstances, the simplest standard methods in nonparametric regression for testing whether a function is constant or linear cannot be applied. We develop a simple general solution which is applicable to nonparametric regression, varying-coefficient models, nonparametric generalized linear models, etc. We show that, in local linear kernel regression, inference about the derived function lambda(.) is facilitated without a loss of power by reparameterization so that lambda(.) is itself a component of Theta(.). Our approach is in contrast with the standard practice of choosing Theta(.) for convenience and allowing lambda(.) to be a non-linear function of Theta(.). The methods are applied to an important data set in nutritional epidemiology.