Abstract:

Let {X_n,n≥1} be an identically distributed NOD random sequence or a strict stationary sequence of m dependent random variables, and f(x) is a probability density function of random variable X₁. Based on NOD samples or m dependent samples, under suitable conditions the kernel estimator for density function f(x) was investigated, and the pointwise strong consistency, the consistency in r order mean and uniform consistency in L₁ were obtained via Fourier transform, the related properties for NOD random sequences and the exponential inequality.

Key words: NOD samples, m dependent samples, kernel estimator, strong consistency, consistency in r order mean