Asymptotically normal explicit estimation of parameters in the Michaelis--Menten equation (Q2773625)

The authors consider the problem of estimation of the unknown parameters \(K>0\) and \(V>0\) for the regressive Michaelis--Menten model NEWLINE\[NEWLINEv_i=Vs_i(K+s_i)^{-1}+\sigma_i\xi_i,\quad i=1,\dots,N,NEWLINE\]NEWLINE where the sequence of independent random variables \(v_i\) is treated as a result of a series of \(N\) trials. The numbers \(s_i\) are assumed to be known. The random variables \(\xi_i\) are i.i.d.\ random variables with \(\mathbf{E}\xi_1=0\) and \(\mathbf{D}\xi_1=1\). The behavior of the variances \(\sigma_i^2\) is assumed to be unknown. Estimators for \(K\) and \(V\) are constructed which are asymptotically normal under rather general assumptions. Conditions for optimality of the estimators are also obtained.NEWLINENEWLINENEWLINEThe article continues two preceding articles of the authors [Sib. Math. J. 41, No. 1, 125-137 (2000; Zbl 0943.62025), and ibid. 42, No. 2, 317-31 (2001; see the preceding review Zbl 0981.62059)].