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• W2101743064 abstract "We consider the wavelet-based estimators of mean regression function with long memory inflnite moving average errors and investigate their asymptotic rates of convergence of estimators based on thresholding of empirical wavelet coe‐cients. We show that these estimators achieve nearly optimal minimax convergence rates within a logarithmic term over a large class of non-smooth functions that involve many jump discontinuities, whose number of discontinuities may grow polynomially fast with sample size. Therefore, in the presence of long memory moving average noise, wavelet estimators still achieve nearly optimal convergence rates and provide explicitly the extraordinary local adaptability in handling discontinuities. A key result in our development is to establish a Bernstein-type exponential inequality for an inflnite weighted sums of i.i.d. random variables under certain cumulant assumption. This large deviation inequality may be of independent interest." @default.
• W2101743064 created "2016-06-24" @default.
• W2101743064 creator A5080125836 @default.
• W2101743064 date "2009-01-01" @default.
• W2101743064 modified "2023-10-16" @default.
• W2101743064 title "Wavelet regression with long memory infinite moving average errors" @default.
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• W2101743064 hasPublicationYear "2009" @default.
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