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A strong law of large numbers for triangular mixingale arrays

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  • de Jong, Robert M.

Abstract

In this paper a strong law of large numbers for triangular mixingale arrays is proven. The mixingale condition is one of asymptotically weak dependence. A strong law of large numbers for triangular mixingale arrays has not been established previously in the literature. The result is applied to kernel regression function estimation.

Suggested Citation

  • de Jong, Robert M., 1996. "A strong law of large numbers for triangular mixingale arrays," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 1-9, March.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:1:p:1-9
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    References listed on IDEAS

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    1. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    2. Davidson, James, 1993. "An L1-convergence theorem for heterogeneous mixingale arrays with trending moments," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 301-304, March.
    3. de Jong, R.M., 1995. "Laws of Large Numbers for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 11(2), pages 347-358, February.
    4. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(2), pages 213-221, June.
    5. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
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    Cited by:

    1. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.

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