Exploring structural characteristics implied in initialdecision making information is an important issue in the process of aggregation. In this paper we provide a new family of aggregation operator called density weig...Exploring structural characteristics implied in initialdecision making information is an important issue in the process of aggregation. In this paper we provide a new family of aggregation operator called density weighted averaging operator（abbreviated as DWA operator）, which carries out the aggregation by classification. In this case, not only the hidden structural characteristics can be identified, some commonly known aggregation operators can also be incorporated into the function of the DWA operator. We further discuss the basic properties of this new operator, such as commutativity, idempotency, boundedness and monotonicity withcertain condition. Afterwards, two important issues related to the DWA operator are investigated, including the arguments partition and the determination of density weights. At last a numerical example regarding performance evaluation of employees is developed to illustrate the using of this new operator.展开更多
Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivat...Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China(71671031,71701040)
文摘Exploring structural characteristics implied in initialdecision making information is an important issue in the process of aggregation. In this paper we provide a new family of aggregation operator called density weighted averaging operator（abbreviated as DWA operator）, which carries out the aggregation by classification. In this case, not only the hidden structural characteristics can be identified, some commonly known aggregation operators can also be incorporated into the function of the DWA operator. We further discuss the basic properties of this new operator, such as commutativity, idempotency, boundedness and monotonicity withcertain condition. Afterwards, two important issues related to the DWA operator are investigated, including the arguments partition and the determination of density weights. At last a numerical example regarding performance evaluation of employees is developed to illustrate the using of this new operator.
基金the National Natural Science Foundation of China (Grant Nos. 10471136, 10671189)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KJCX3-SYW-S02)
文摘Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.
