On asymptotics related to the statistical curvatures in nonlinear regression (Q1175999)

\textit{B. Efron} [Ann. Stat. 3, 1189-1242 (1975; Zbl 0321.62013)] and \textit{S. Amari} [ibid. 10, 357-385 (1982; Zbl 0507.62026)] have studied several asymptotic properties related to the statistical curvatures for a specific curved exponential family in which the samples are independent and identically distributed and the curvatures are defined in a fixed space. We study the similar asymptotics for nonlinear regression, but there are two substantial differences from the family studied by Efron and Amari. First, the nonlinear regression is generated by independent but not identically distributed samples. Second, the enveloping space, in which the solution locus is located, is related to the sample size in nonlinear regression. The method of stochastic expansions developed by \textit{B. Wei} [Acta Math. Appl. Sin., Engl. Ser. 5, No. 3, 269-278 (1989; Zbl 0697.62052)] is frequently used in this note.