For different classes of deterministic and random sampling (t(k)), we establish the asymptotic expressions for the bias and the variance of the estimate r(n)(x) based on sampled data (X-tk, Y-tk)k=1,...,n for the regr...
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For different classes of deterministic and random sampling (t(k)), we establish the asymptotic expressions for the bias and the variance of the estimate r(n)(x) based on sampled data (X-tk, Y-tk)k=1,...,n for the regression function r(x) = E(Y-t/X-t = x) of unbounded continuous-time processes (X-t, Y-t)(t is an element of R) (not necessarily stationary). Under mild mixing conditions, we show that r(n)(x) has exactly the same asymptotic quadratic error as in the i.i.d. case. In order to prove this result, we use some large deviations inequalities for mixingprocesses.
Let Z = (X, Y)= {Z(t)} t∈ℛ be a stationary continuous-time process taking values in ℛ. By means of the corresponding discrete-time process {X(t i ), Y(t i )} i=1 n, sampled at random instants {t i }, a nonparametric ...
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