摘要
Multivariate longitudinal data arise frequently in a variety of applications,where multiple outcomes are measured repeatedly from the same subject.In this paper,we first propose a two-stage weighted least square estimation procedure for the regression coefficients when the random error follows an irregular autoregressive(AR)process,and establish asymptotic normality properties for the resulting estimators.We then apply the smoothly clipped absolute deviation(SCAD)variable selection approach to determine the order of the AR error process.We further propose a test statistic to check whether multiple responses are correlated at the same observation time,and derive the asymptotic distribution of the proposed test statistic.Several simulated examples and real data analysis are presented to illustrate the finite-sample performance of the proposed method.
基金
supported by the Fundamental Research Funds of Shandong University(Grant No.2018GN050)
the Academic Prosperity Program provided by School of Economics,Shandong University and the Taishan Scholar Program of Shandong Province
supported by National Natural Science Foundation of China(Grant No.11871323)
the State Key Program in the Major Research Plan of National Natural Science Foundation of China(Grant No.91546202)
Program for Innovative Research Team of Shanghai University of Finance and Economics。
