Empirical Likelihood for a Heteroscedastic Partial Linear Model
Empirical Likelihood for a Heteroscedastic Partial Linear Model
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DOI：
10.1080/03610921003597229
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发表时间：
2011-02
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影响因子：
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通讯作者：
Guoliang Fan;Han-Ying Liang;Hongxia Xu
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文献类型：
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作者：
Guoliang Fan;Han-Ying Liang;Hongxia Xu
考虑异方差回归模型，其中β是未知参数的p × 1列向量，（Xi，Ti，Zi）是随机设计点，Yi是响应变量，g（·）是定义在闭区间[0，1]上的未知函数，{ei，Zi}是鞅差序列.当f是已知和未知的情况下，我们提出了参数β的经验对数似然比统计量。对于每一种情况，导出了Wilks定理的非参数形式。然后使用结果来构造参数的置信区域。仿真研究表明，经验似然方法的性能优于正常的近似为基础的方法。
Consider the heteroscedastic regression model , where , β is a p × 1 column vector of unknown parameter, (X i , T i , Z i ) are random design points, Y i are the response variables, g(·) is an unknown function defined on the closed interval [0, 1], {e i , ℱ i } is a sequence of martingale differences. When f is known and unknown cases, we propose the empirical log-likelihood ratio statistics for the parameter β. For each case, a nonparametric version of Wilks' theorem is derived. The results are then used to construct confidence regions of the parameter. Simulation study shows that the empirical likelihood method performs better than a normal approximation-based approach.