Nonlinear least-squares estimation

By D. Pollard, Peter Radchenko. 2006

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Statistical inference for dynamical systems: A review (2012, methodology): “In particular, by the product rule, one typically expects that in hyperbolic dynamical systems the derivatives ∂aT k a (x) will grow exponentially as a function of k, and such growth implies that the estimates of [135] cannot be used even to show consistency.”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, unknown): “Since the differential equations setting is covered by the general theory of nonlinear least squares, theoretical results available for the latter apply also in the differential equations setting and we refer for example, to [25] and [57], or more generally to [43, 44], and [33] for a thorough treat”
Folklore Theorems, Implicit Maps, and Indirect Inference (2012, background): “…orders, such as in systems with cointegrated regressors (Park and Phillips, 1988; Phillips, 1988), systems with slowly varying trend regressors or nonlinear trends (Phillips, 2007; Pollard and Radchenko, 2006), and systems with co-explosive processes (Phillips and Magdalinos, 2008; Nielsen, 2009).”