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Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains

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  • Senoussi, R.

Abstract

In the first part, we establish an upper bound of an iterated logarithm law for a sequence of processes endowed with the uniform convergence on compacts, where Mn(x) is a square integrable martingale for each x in . In the second part we present an iterative kernel estimator of the driving function f of the regression model:Xn+1=f(Xn)+[var epsilon]n+1.Strong convergences and CLT results are proved for this estimator and then extended to controlled Markov models.

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  • 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.
    • Handle: RePEc:eee:spapps:v:89:y:2000:i:2:p:193-211
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    References listed on IDEAS

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    1. Masry, Elias & Györfi, László, 1987. "Strong consistency and rates for recursive probability density estimators of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 79-93, June.
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    Cited by:

    1. Loukianova, D. & Loukianov, O., 2005. "Uniform law of large numbers and consistency of estimators for Harris diffusions," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 347-355, October.
    2. 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.

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