THE STRONG UNIFORM CONSISTENCY OF KERNEL DENSITY ESTIMATES FOR φ—MIXING SAMPLE

Let X_1, X_2, … be a φ-mixing Sample with density function f(x), f_n(x_1 K_n)= be an estimate of the f(x), under proper conditions, we obtain he best convergence rate sup|f_n(x,K_)-f(x)|=0((n/logn)~(-1/3)), a.s..