Penalized Multiply Robust Estimation in AR(p) Processes with Missing
Explanatory Variables via True Structure Candidate Specifications
 
   Lead Investigator:    Wei Xiong
   Institution      :    Schoolof Mathematics, Jilin University
   E-Mail           :    xiongwei16@mails.jlu.edu.cn
   Proposal ID      :    1562



   Proposal Description:
   Our aim is to finding a multiply robust estimator for the parameter in  high-order autoregressive model, which has an incomplete explanatory variable. The model is excepted from the person who accepted the mini-mental state examination (MMSE). X_t (t>=0) is the result of MMSE in t-th month, it has the following construction: X_t=\sum^p_{i=1}\alpha_i X_{t-i}+\beta_t                 Z_t+\epsilon_t, where (\alpha_1,...,\alpha_p) is sparse. The explanatory         variable Z_t denotes the dementia status (also can be replaced by other           significant effect variable) of the subject at that time, which can't be always observed. We used the database of some subject to estimate the parameter in the model. The creative point of our research is that the candidate model set of the response mechanism and p(Z_t|X_t,X_{t-1},...) only contain the structure high-dimensional sparse parameter), and we proposed a novel penalized multiply robust estimation equation (PMREE). The selecting criterion for optimal tuning parameters in PMREE are modified from previously criteria. The method will be fitted for other longitudinal situations in clinical analysis.