ABSTRACT
The notion of local asymptotic normality of a sequence of statistical models (hereafter also called “experiments”) was introduced in the seminal paper “Locally asymptotically normal families of distributions” by Le Cam (1960). That paper figures among the best-known contributions of Lucien Le Cam to mathematical statistics. Part of his work has been presented in the more recent paper by van der Vaart (2002). The Le Cam asymptotic theory of experiments, and in particular the Local Asymptotic Normality (LAN) property, is the backbone of many different recent contributions to the statistical literature. LAN-type results have been established or used in many different statistical contexts on R p $ {\mathbb{R}}^{p} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119472/5ff6ea01-2f47-4320-8bbe-e544021cff79/content/inline-math5_2.tif"/> :
Time series: long disturbances (Hallin et al. 1999), efficient estimation in nonlinear autoregressive models (Koul & Schick 1997), multivariate ARMA models (Garel & Hallin 1995, Hallin & Paindaveine 2004), unit root tests (Hallin et al. 2011) and GARCH models (Francq &Zakoian 2004,2012, 2012).
Semiparametric models: general results (Bickel et al. 1993, Choi et al. 1996, Hallin & Werker 2003), copula models (Genest & Werker 2002, Chen et al. 2006, Segers et al. 2014), inference for elliptical distributions with emphasis on the location parameter (Hallin & Paindaveine 2002), on the scatter parameter (Hallin & Paindaveine 2006) and on Principal Component Analysis (Hallin et al. 2010).
Infinite dimensional models: efficiency in non-parametric models (Begun et al. 1983) and, very recently, inference for high-dimensional models (Onatski et al. 2013,2014, Cutting et al.2017a).
