Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series
A general framework is proposed for (auto)regression nonparametric estimationof recurrent time series in a class of Hilbert Markov processes with a Lipschitzconditional mean. This includes various nonstationarities by relaxing usual dependenceassumptions as mixing or ergodicity, which are replaced with recurrence. The cornerstoneof design-adaptation is a data-driven bandwidth choice based on an empirical biasvariance tradeoff, giving rise to a random consistency rate for a uniform kernel estimator.The estimator converges with this random rate, which is the optimal minimaxrandom rate over the considered class of recurrent time series. Extensions to general kernelestimators are investigated. For weak dependent time-series, the order of the randomrate coincides with the deterministic minimax rate previously derived. New deterministicestimation rates are obtained for modified Box-Cox transformations of Random Walks.
|Date of creation:||2004|
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- Yakowitz, Sid, 1993. "Nearest neighbor regression estimation for null-recurrent Markov time series," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 311-318, November.
- Yakowitz, Sidney & Györfi, László & Kieffer, John & Morvai, Gusztáv, 1999. "Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 24-41, October.
- Emmanuel Guerre & Jules Maes, 1998. "Optimal Rate for Nonparametric Estimation in Deterministic Dynamical Systems," Working Papers 98-06, Centre de Recherche en Economie et Statistique.
- E. Guerre & J. Maës, 1998. "Optimal Rate for Nonparametric Estimation in Deterministic Dynamical Systems," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 157-173, May.
- Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
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