Arbeitspapier
Parametric estimation: Finite sample theory
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.
- Sprache
-
Englisch
- Erschienen in
-
Series: SFB 649 Discussion Paper ; No. 2011-081
- Klassifikation
-
Wirtschaft
Estimation: General
Semiparametric and Nonparametric Methods: General
- Thema
-
maximum likelihood
local quadratic approximation
concentration
coverage
deficiency
Zeitreihenanalyse
Schätztheorie
Theorie
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Spokoiny, Vladimir
- Ereignis
-
Veröffentlichung
- (wer)
-
Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
- (wo)
-
Berlin
- (wann)
-
2011
- Handle
- Letzte Aktualisierung
-
20.09.2024, 08:23 MESZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Spokoiny, Vladimir
- Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
Entstanden
- 2011
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