M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the...M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the upper and lower bounds of the smoothing parameter selected by the proposed criterion are established. The main contribution of this study shows a drastic difference from those encountered in the classical L2-, L1- cross-validation technique, which leads only to the consistency in the sense of the average. Obviously, our results are novel and nontrivial from the point of view of mathematics and statistics, which provides insight and possibility for practitioners substituting maximum deviation for average deviation to evaluate the performance of the data-driven technique.展开更多
In this paper Hill's equation is discussed. A new discriminant of Hill's equation is obtained, whose convergent rate is faster than that of traditional discriminant. The results obtained generalizes ones of th...In this paper Hill's equation is discussed. A new discriminant of Hill's equation is obtained, whose convergent rate is faster than that of traditional discriminant. The results obtained generalizes ones of the papers [2] and [3].展开更多
文摘M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the upper and lower bounds of the smoothing parameter selected by the proposed criterion are established. The main contribution of this study shows a drastic difference from those encountered in the classical L2-, L1- cross-validation technique, which leads only to the consistency in the sense of the average. Obviously, our results are novel and nontrivial from the point of view of mathematics and statistics, which provides insight and possibility for practitioners substituting maximum deviation for average deviation to evaluate the performance of the data-driven technique.
文摘In this paper Hill's equation is discussed. A new discriminant of Hill's equation is obtained, whose convergent rate is faster than that of traditional discriminant. The results obtained generalizes ones of the papers [2] and [3].
