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Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models

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  • Nadine Hilgert
  • Bruno Portier

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  • Nadine Hilgert & Bruno Portier, 2012. "Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 105-125, July.
    • Handle: RePEc:spr:sistpr:v:15:y:2012:i:2:p:105-125
    DOI: 10.1007/s11203-012-9065-7
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    References listed on IDEAS

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    1. Eckhard Liebscher, 1999. "Estimating the Density of the Residuals in Autoregressive Models," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 105-117, May.
    2. Bachmann, Dirk & Dette, Holger, 2005. "A note on the Bickel-Rosenblatt test in autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 221-234, October.
    3. Fuxia Cheng, 2010. "Global property of error density estimation in nonlinear autoregressive time series models," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 43-53, April.
    4. Senoussi, R., 2000. "Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 193-211, October.
    5. Lee, Sangyeol & Na, Seongryong, 2002. "On the Bickel-Rosenblatt test for first-order autoregressive models," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 23-35, January.
    6. Ahmad, Ibrahim A., 1992. "Residuals density estimation in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 133-139, May.
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