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http://hdl.handle.net/10419/56754
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| Title: | | Parametric estimation: Finite sample theory  |
| Authors: | | Spokoiny, Vladimir |
| Issue Date: | | 2011 |
| Series/Report no.: | | SFB 649 discussion paper 2011-081 |
| Abstract: | | 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. |
| Subjects: | | maximum likelihood local quadratic approximation concentration coverage deficiency |
| JEL: | | C13 C14 |
| Document Type: | | Working Paper |
| Appears in Collections: | | SFB 649 Discussion Papers, HU Berlin
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