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On asymptotic inference in stochastic differential equations with time‐varying covariates
Author(s) -
Maitra Trisha,
Bhattacharya Sourabh
Publication year - 2018
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11471
Subject(s) - asymptotic distribution , consistency (knowledge bases) , estimator , covariate , mathematics , stochastic differential equation , statistical inference , population , inference , bayesian inference , normality , strong consistency , bayesian probability , statistics , econometrics , computer science , artificial intelligence , medicine , geometry , environmental health
In this article, we introduce a system of stochastic differential equations ( SDE s) consisting of time‐dependent covariates and consider both fixed and random effects. We also allow the functional part associated with the drift function to depend upon unknown parameters. For this general SDE system we establish consistency and asymptotic normality of the maximum likelihood estimator. We consider a Bayesian approach for learning about the population parameters, and prove consistency and asymptotic normality of the corresponding posterior distribution. We supplement our theoretical investigation with simulated and real data analyses, obtaining encouraging results in both cases. The Canadian Journal of Statistics 46: 635–655; 2018 © 2018 Statistical Society of Canada