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Nearest neighbor regression estimation for null-recurrent Markov time series

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  • Yakowitz, Sid

Abstract

The past few years have witnessed the emergence of a vigorous literature seeking to exploit nonparametric estimation ideas in time-series contexts. As documented herein, in recent times, various mixing conditions postulated in the seminal investigations by Rosenblatt (1970) and Roussas (1969) have been relaxed. The present study assumes that the observed series is Markov with a time-invariant transition function, but does not postulate mixing conditions or that the coordinate process have a proper probability distribution. Thereby, our methodology encompasses random walks, for example. Nevertheless, a variation of the traditional nearest neighbor regression estimate is found to be pointwise consistent under useful conditional moment assumptions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:2:p:311-318
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    Citations

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    Cited by:

    1. Arjen Hussem & Casper Ewijk & Harry Rele & Albert Wong, 2016. "The Ability to Pay for Long-Term Care in the Netherlands: A Life-cycle Perspective," De Economist, Springer, vol. 164(2), pages 209-234, June.
    2. Karlsen, Hans Arnfinn & Tjostheim, Dag, 1998. "Nonparametric estimation in null recurrent times series," SFB 373 Discussion Papers 1998,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Albert Wong & Hendriek Boshuizen & Johan Polder & José António Ferreira, 2017. "Assessing the inequality of lifetime healthcare expenditures: a nearest neighbour resampling approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 141-160, January.
    4. 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.
    5. 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.
    6. Algoet, Paul & Györfi, László, 1999. "Strong Universal Pointwise Consistency of Some Regression Function Estimates," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 125-144, October.
    7. Sancetta, Alessio, 2009. "Nearest neighbor conditional estimation for Harris recurrent Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2224-2236, November.
    8. Emmanuel Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series," Working Papers 2004-22, Center for Research in Economics and Statistics.
    9. Arjen Hussem & Casper Ewijk & Harry Rele & Albert Wong, 2016. "The Ability to Pay for Long-Term Care in the Netherlands: A Life-cycle Perspective," De Economist, Springer, vol. 164(2), pages 209-234, June.
    10. Guerre, Emmanuel, 2000. "Design Adaptive Nearest Neighbor Regression Estimation," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 219-244, November.

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