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
The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the p...The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications （together with the notion of a weak p-convergent operator, which we introduce in the present paper） to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.展开更多
The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Ta...The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .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.
基金Supported by the National Research Foundation of South Africa(Grant Nos.85619 and 101265)
文摘The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications （together with the notion of a weak p-convergent operator, which we introduce in the present paper） to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.
文摘The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .
