For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How ...For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.展开更多
This paper discusses a randomized Logistic equation N（t）=（r+αB（t））N（t）[1-（N（t）/K）] with an initial value N（0）=N<sub>0</sub>,and N<sub>0</sub> is a random variable satisfying 0＜N...This paper discusses a randomized Logistic equation N（t）=（r+αB（t））N（t）[1-（N（t）/K）] with an initial value N（0）=N<sub>0</sub>,and N<sub>0</sub> is a random variable satisfying 0＜N<sub>0</sub>＜K.The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate（MLE）of the parameters of the equation are studied.展开更多
In epidemiological and clinical studies,the restricted mean lifetime is often of direct interest quantity.The differences of this quantity can be used as a basis of comparing several treatment groups with respect to t...In epidemiological and clinical studies,the restricted mean lifetime is often of direct interest quantity.The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times.When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring,the imbalances in confounding factors need to be accounted.We use the mixture of additive hazards model and inverse probability of censoring weighting method to estimate the differences of restricted mean lifetime.The average causal effect is then obtained by averaging the differences in fitted values based on the additive hazards models.The asymptotic properties of the proposed method are also derived and simulation studies are conducted to demonstrate their finite-sample performance.An application to the primary biliary cirrhosis(PBC)data is illustrated.展开更多
基金supported by the National Natural Science Foundation of China(No.12271370)。
文摘For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10431010 and 10571021)the Key Laboratory for Applied Statistics of Ministry of Education of China(KLAS)
文摘This paper discusses a randomized Logistic equation N（t）=（r+αB（t））N（t）[1-（N（t）/K）] with an initial value N（0）=N<sub>0</sub>,and N<sub>0</sub> is a random variable satisfying 0＜N<sub>0</sub>＜K.The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate（MLE）of the parameters of the equation are studied.
基金partly supported by the National Natural Science Foundation of China(11671268,11771431 and 11690015)the Key Laboratory of RCSDS,CAS(2008DP173182)。
文摘In epidemiological and clinical studies,the restricted mean lifetime is often of direct interest quantity.The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times.When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring,the imbalances in confounding factors need to be accounted.We use the mixture of additive hazards model and inverse probability of censoring weighting method to estimate the differences of restricted mean lifetime.The average causal effect is then obtained by averaging the differences in fitted values based on the additive hazards models.The asymptotic properties of the proposed method are also derived and simulation studies are conducted to demonstrate their finite-sample performance.An application to the primary biliary cirrhosis(PBC)data is illustrated.
