Abstract
A strong law of large numbers for a triangular array of strictly stationary associated random variables is proved. It is used to derive the pointwise strong consistency of kernel type density estimator of the one-dimensional marginal density function of a strictly stationary sequence of associated random variables, and to obtain an improved version of a result by Van Ryzin (1969) on the strong consistency of density estimator for a sequence of independent and identically distributed random variables.
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Dewan, I., Rao, B.L.S.P. Remarks on the strong law of large numbers for a triangular array of associated random variables. Metrika 45, 225–234 (1997). https://doi.org/10.1007/BF02717105
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DOI: https://doi.org/10.1007/BF02717105