Irrespective of the statistical model under study, the derivation of lim- its, in the Le Cam sense, of sequences of local experiments (see -) often follows along very similar lines, essentially involving differentiability in quadratic mean of square roots of (conditional) densities. This chapter establishes two ab- stract and very general results providing sufficient and nearly necessary conditions for (i) the existence of a quadratic expansion, and (ii) the asymptotic linearity of local log-likelihood ratios (asymptotic linearity is needed, for instance, when un- specified model parameters are to be replaced, in some statistic of interest, with some preliminary estimator). Such results have been established, for locally asymp- totically normal (LAN) models involving independent and identically distributed observations, by, e.g., ,  and . Similar results are provided here for mod- els exhibiting serial dependencies which, so far, have been treated on a case-by-case basis (see  and  for typical examples) and, in general, under stronger regularity assumptions. Unlike their i.i.d. counterparts, our results extend beyond the context of LAN experiments, so that non-stationary unit-root time series and cointegration models, for instance, also can be handled (see ).
|Title of host publication||Mathematical Statistics and Limit Theorems |
|Subtitle of host publication||Festschrift in Honour of Paul Deheuvels|
|Editors||M. Hallin, D.M. Mason, D. Pfeifer, J. Steinebach|
|Place of Publication||Cham|
|Number of pages||19|
|Publication status||Published - 8 Apr 2015|
|Name||Springer Proceedings in Mathematics & Statistics|