x Preface
illustrative examples. In our opinion, the sufficient prerequisite is a stan-
dard course in advanced probability supported by undergraduate statistics
and real analysis. We hope that students who successfully pass this course
are prepared for reading original papers and monographs in the minimax
estimation theory and can be easily introduced to research studies in this
This book is organized into three parts. Part 1 is comprised of Chap-
ters 1-7 that contain fundamental topics of local asymptotic normality as
well as irregular statistical models, change-point problem, and sequential
estimation. For convenience of reference we also included a chapter on clas-
sical parametric linear regression with the concentration on the asymptotical
properties of least-squares estimators. Part 2 (Chapters 8-12) focuses on es-
timation of nonparametric regression functions. We restrict the presentation
to estimation at a point and in the quadratic and uniform norms, and con-
sider deterministic as well as random designs. The last part of the book,
Chapters 13-16, is devoted to special more modern topics such as influence of
higher-dimension and structure in nonparametric regression models, prob-
lems of adaptive estimation, and testing of nonparametric hypotheses. We
present the ideas through simple examples with the equidistant design.
Most chapters are weakly related to each other and may be covered in
any order. Our suggestion for a two-semester course would be to cover the
parametric part during the first semester and to cover the nonparametric
part and selected topics in the second half of the course.
We are grateful to O. Lepskii for his advice and help with the presenta-
tion of Part 3.
The authors, October 2010
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