On asymptotically optimal wavelet estimation of trend functions under long-range dependence
On asymptotically optimal wavelet estimation of trend functions under long-range dependence
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DOI：
10.3150/10-bej332
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发表时间：
2012-02
期刊：
影响因子：
1.5
通讯作者：
J. Beran;Yevgen Shumeyko
中科院分区：
文献类型：
--
作者：
J. Beran;Yevgen Shumeyko
研究了具有强相关高斯残差的时间序列模型中趋势函数的数据自适应小波估计。导出了最优平均积分平方误差的渐近表达式以及相应的最优平滑和分辨率参数。由于自适应底层趋势函数的性质，该方法对光滑趋势函数表现出很好的性能，同时对不连续函数保持极大极小小波估计的竞争力。仿真说明了渐近结果和有限样本行为。
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and resolution parameters are derived. Due to adaptation to the properties of the underlying trend function, the approach shows very good performance for smooth trend functions while remaining competitive with minimax wavelet estimation for functions with discontinuities. Simulations illustrate the asymptotic results and finite-sample behavior.