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Abstract:
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Consider a nonparametric regression model y(i) = m(t(i)) + u(i), i=1,2,...,n. Here y(i) denotes time series with long-range dependence, t(i) = i/n is rescaled time and m is an unknown but smooth trend function that satisfies some regularity conditions. The regression errors u(i) have zero mean, finite variance and are assumed to be Gaussian subordinated. Specifically, let u(i) = G(Z(i), t(i)), where G is well-defined but unknown and Z(i) denotes a latent Gaussian process with long-memory. Due to this assumption, the cumulative distribution function F of the regression errors may have a varying shape over time. In particular, F may be non-Gaussian. We address estimation of F using a kernel K that is a symmetric probability density function satisfying some moment conditions. In addition we let K have an absolutely integrable characteristic function. We consider Priestley-Chao regression estimates for m and F and provide simple proof of weak uniform consistency. The special case where G is monotone is also considered.
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