8 Pages

Parameter estimation for high dimensional ordinary differential equation

WithH. Xue, P. Linel, J. Chen, Y.X. Yuan & H. Wu

In reality, X(t) cannot be measured exactly and d rectly; instead, its surrogate Y can be measured. For simplicity, here we assume an additive measurement

error model to describe the relationship between X(ti) and the surrogate Yi,

= +∈( ) ,Y X ti i i (2)

at random or fixed design time points , ,1t tn , where the measurement errors ( ,  ,  )1 nε ε are independent with mean zero and a diagonal variancecovariance matrix Σ. Moreover, in the case of random design, assume that the measurement errors are independent of X(t).