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The problem of error density estimation for a functional single index modelwith dependent errors is studied. A Bayesian method is utilized tosimultaneously estimate the bandwidths in the kernel-form error density andregression function, under an autoregressive error structure. For estimatingboth the regression function and error density, empirical studies show that thefunctional single index model gives improved estimation and predictionaccuracies than any nonparametric functional regression considered.Furthermore, estimation of error density facilitates the construction ofprediction interval for the response variable.

Estimation of a functional single index model with dependent errors and unknown error density