One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient fun...One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.展开更多
To date, Wald sequential probability ratio test(WSPRT) has been widely applied to track management of multiple hypothesis tracking(MHT). But in a real situation, if the false alarm spatial density is much larger than ...To date, Wald sequential probability ratio test(WSPRT) has been widely applied to track management of multiple hypothesis tracking(MHT). But in a real situation, if the false alarm spatial density is much larger than the new target spatial density, the original track score will be very close to the deletion threshold of the WSPRT. Consequently, all tracks, including target tracks, may easily be deleted, which means that the tracking performance is sensitive to the tracking environment. Meanwhile, if a target exists for a long time, its track will have a high score, which will make the track survive for a long time even after the target has disappeared. In this paper, to consider the relationship between the hypotheses of the test, we adopt the Shiryayev SPRT(SSPRT) for track management in MHT. By introducing a hypothesis transition probability, the original track score can increase faster, which solves the first problem. In addition, by setting an independent SSPRT for track deletion, the track score can decrease faster, which solves the second problem. The simulation results show that the proposed SSPRT-based MHT can achieve better tracking performance than MHT based on the WSPRT under a high false alarm spatial density.展开更多
基金supported by National Natural Science Foundation of China under Grant No.1117112the Fund of Shanxi Datong University under Grant No.2010K4+1 种基金the Doctoral Fund of Ministry of Education of China under Grant No.20090076110001National Statistical Science Research Major Program of China under Grant No.2011LZ051
文摘One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.
基金supported by National Natural Science Foundation of China (Grant Nos. 61471019, 61501011)
文摘To date, Wald sequential probability ratio test(WSPRT) has been widely applied to track management of multiple hypothesis tracking(MHT). But in a real situation, if the false alarm spatial density is much larger than the new target spatial density, the original track score will be very close to the deletion threshold of the WSPRT. Consequently, all tracks, including target tracks, may easily be deleted, which means that the tracking performance is sensitive to the tracking environment. Meanwhile, if a target exists for a long time, its track will have a high score, which will make the track survive for a long time even after the target has disappeared. In this paper, to consider the relationship between the hypotheses of the test, we adopt the Shiryayev SPRT(SSPRT) for track management in MHT. By introducing a hypothesis transition probability, the original track score can increase faster, which solves the first problem. In addition, by setting an independent SSPRT for track deletion, the track score can decrease faster, which solves the second problem. The simulation results show that the proposed SSPRT-based MHT can achieve better tracking performance than MHT based on the WSPRT under a high false alarm spatial density.
