摘要
Under quite mild conditions onk n . the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified nearest neighbor kernel regression of an a-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is $\sum\limits_{j = 1}^\infty {j^{a - 1} a(j)^{1 - 1/v}< \infty (a > 1} $ , $v > 1) or \sum\limits_{j = 1}^\infty {j^{a - 1} a(j)< \infty (a > 1} )$ . which is simple and weak.
Under quite mild conditions on k n , the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified nearest neighbor kernel regression of an α mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is ∑∞j=1j a-1 α(j) 1-1/ν <∞(a>1, ν>1) or ∑∞j=1j a-1 α(j)<∞(a>1), which is simple and weak.
