Uniform Strong Convergence of Kernel-Type Estimators for m-LENQD Sequences with Applications
In this paper, we firs tderiv eth eunifor mstron gconsistenc yan dth ecorrespondin gconvergence rates for kernel estimators of both the distribution function and the probability density function for sequences of m-linearly extended negative quadrant dependent (m-LENQD) random variables under mild regularity conditions. The obtained results significantl yimprov ean dexten dexisting ones in the literature. As their theoretical applications, we further establish the uniform strong consistency and convergence rates for estimators of the hazard rate function and the mode of the density function. Numerical simulations and a real data analysis are conducted to assess the finite- sample performance of the proposed estimators, confirmin gth easymptoti cpropertie sderive din the theoretical analysis.