Weakly differentiable functions
Weakly differentiable functions
Random Iterative Models
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
Conditional estimation for dependent functional data
Journal of Multivariate Analysis
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This paper is concerned with consistent nearest neighbor time series estimation for data generated by a Harris recurrent Markov chain on a general state space. It is shown that nearest neighbor estimation is consistent in this general time series context, using simple and weak conditions. The results proved here, establish consistency, in a unified manner, for a large variety of problems, e.g. autoregression function estimation, and, more generally, extremum estimators as well as sequential forecasting. Finally, under additional conditions, it is also shown that the estimators are asymptotically normal.