000			01700nam a22001817a 4500
008			221028b2021 |||||||| |||| 00| 0 eng d
020			_a9781108994132
082			_a519.54 GIN-E
100			_aGine, Evarist
245			_aMathematical foundations of infinite-dimensional statistical models / _cEvarist Gine and Richard Nickl
260			_aUnited Kingdom _bCambridge University Press _c2021
300			_a690 p.
365			_aGBP _b39.99.
500			_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, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is 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 a 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. Winner of the 2017 PROSE Award for Mathematics.
650			_aNonparametric statistics
650			_aFunction spaces
700			_aNickl, Richard
999			_c83223 _d83223