Parametric estimation: Finite sample theory

Arbeitspapier

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are: (1) the study is non-asymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly misspecified and the underlying data distribution can lie beyond the given parametric family. The main results include a large deviation bounds for the (quasi) maximum likelihood and the local quadratic majorization of the log-likelihood process. The latter yields a number of important corollaries for statistical inference: concentration, confidence and risk bounds, expansion of the maximum likelihood estimate, etc. All these corollaries are stated in a non-classical way admitting a model misspecification and finite samples. However, the classical asymptotic results including the efficiency bounds can be easily derived as corollaries of the obtained non-asymptotic statements. The general results are illustrated for the i.i.d. set-up as well as for generalized linear and median estimation. The results apply for any dimension of the parameter space and provide a quantitative lower bound on the sample size yielding the root-n accuracy.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2011-081

Classification and Topics

• Classification: Wirtschaft ; Estimation: General ; Semiparametric and Nonparametric Methods: General
• Subject: maximum likelihood ; local quadratic approximation ; concentration ; coverage ; deficiency ; Zeitreihenanalyse ; Schätztheorie ; Theorie

Contributors, Location and Time

• Event: Geistige Schöpfung
• (who): Spokoiny, Vladimir
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/56754
• Last update: 20.09.2024, 8:23 AM CEST