Abstract
In this paper, we primarily focus on the edge frequency polygon estimator of f ( x ) , which represents the probability density function of a sequence of φ-mixing random variables { X i , i ≥ 1 } . We establish the uniformly strong consistency and the convergence rate of asymptotic normality for the edge frequency polygon estimator under suitable conditions. Notably, the convergence rate achieves O ( n − 1 / 6 ) , which is more precise compared to the corresponding rate mentioned in the existing literature. Additionally, we present simulation studies to validate the theoretical results.
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