Convergence test statistic of kernel estimators of a density function from stationary sequence of strongly linearly positive quadrant dependent random variables

In this paper we will consider convergence test statistic of an estimator of a density function of stationary sequence of strongly linearly positive quadrant dependent random variables. Considered the statistic is constructed based on the kernel estimate of the density function. We will prove an invariance principle for the kernel density estimator from stationary sequences strongly linearly positive quadrant dependent random variables.

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