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Mathematical Foundations of Infinite-Dimensional Statistical Models (Hardcover)
Loot Price: R2,702
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Mathematical Foundations of Infinite-Dimensional Statistical Models (Hardcover)
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Expected to ship within 12 - 17 working days
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In 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.
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