| 000 | 02482nam a2200373 i 4500 | ||
|---|---|---|---|
| 001 | CR9781107337862 | ||
| 003 | UkCbUP | ||
| 005 | 20240912200940.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr|||||||||||| | ||
| 008 | 130212s2016||||enk o ||1 0|eng|d | ||
| 020 | _a9781107337862 (ebook) | ||
| 020 | _z9781107043169 (hardback) | ||
| 040 |
_aUkCbUP _beng _erda _cUkCbUP |
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| 050 | 0 | 0 |
_aQA278.8 _b.G56 2016 |
| 082 | 0 | 0 |
_a519.5/4 _223 |
| 100 | 1 |
_aGiné, Evarist, _d1944- _eauthor. |
|
| 245 | 1 | 0 |
_aMathematical foundations of infinite-dimensional statistical models / _cEvarist Giné, Richard Nickl. |
| 264 | 1 |
_aCambridge : _bCambridge University Press, _c2016. |
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| 300 |
_a1 online resource (xiv, 690 pages) : _bdigital, PDF file(s). |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aCambridge series on statistical and probabilistic mathematics ; _v40 |
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| 500 | _aTitle from publisher's bibliographic system (viewed on 10 Dec 2015). | ||
| 520 | _aIn nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In the final chapter, the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. | ||
| 650 | 0 | _aNonparametric statistics. | |
| 650 | 0 | _aFunction spaces. | |
| 700 | 1 |
_aNickl, Richard, _d1980- _eauthor. |
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| 776 | 0 | 8 |
_iPrint version: _z9781107043169 |
| 830 | 0 |
_aCambridge series on statistical and probabilistic mathematics ; _v40. |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1017/CBO9781107337862 |
| 942 |
_2ddc _cEB |
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| 999 |
_c10001 _d10001 |
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