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Abstract:
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Consider observations Y(i), i=1,2,..,n, where i denotes time. The cumulative distribution function at time i is: F_i(y) = P(Y(i) < y), where, Y(i) and y are real. Of particular interest are F_i(y) and other related quantities, such as the moment generating function M_i(t) = E(exp(tY(i))), where t is real. In particular, when F_i(y) = F(y), the shape of the distribution function remains unchanged over time.
We consider estimation using kernel smoothing and some asymptotic results, under standard conditions and a given correlation structure, and in particular, long-range dependence. This problem has implications for various fields of science, including certain domains of climate change research, where long-term geophysical records are used for inference concerning past climate conditions.
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