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Nonparametric Estimation of Probability Densities and Regression Curves

Author: E A Nadaraya
Publisher: Dordrecht : Springer Netherlands, 1989.
Series: Mathematics and its Applications (Soviet Series), 20.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
'Et moi ..., si. j'avail su comment en revenir. One service mathematics has rendered!be human race. It has put common sense back jc n'y scrais point a1U: where it belongs, on the topmost sbelf next Jules Verne to \be dusty canister labelled 'discarded non- TIle series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: E A Nadaraya
ISBN: 9789400925830 9400925832
OCLC Number: 851370448
Description: 1 online resource (228 pages).
Contents: 1. Asymptotic Properties of Certain Measures of Deviation for Kernel-Type Non Parametric Estimators of Probability Densities --
1. Integrated Mean Square Error of Nonparametric Kernel-Type Probability Density Estimators --
2. The Mean Square Error of Nonparametric Kernel-Type Density Estimators --
2. Strongly Consistent in Functional Metrics Estimators of Probability Density --
1. Strong Consistency of Kernel-Type Density Estimators in the Norm of the Space C --
2. Convergence in the L2 Norm of Kernel-Type Density Estimators --
3. Convergence in Variation of Kernel-Type Density Estimators and its Application to a Nonparametric Estimator of Bayesian Risk in a Classification Problem --
3. Limiting Distributions of Deviations of Kernel-Type Density Estimators --
1. Limiting Distribution of Maximal Deviation of Kernel-Type Estimators --
2. Limiting Distribution of Quadratic Deviation of Two Nonparametric Kernel-Type Density Estimators --
3. The Asymptotic Power of the Un1n2-Test in the Case of' singular' Close Alternatives --
4. Testing for Symmetry of a Distribution --
5. Independence of Tests Based on Kernel-Type Density Estimators --
4. Nonparametric Estimation of the Regression Curve and Components of a Convolution --
1. Some Asymptotic Properties of Nonparametric Estimators of Regression Curves --
2. Strong Consistency of Regression Curve Estimators in the Norm of the Space C(a, b) --
3. Limiting Distribution of the Maximal Deviation of Estimators of Regression Curves --
4. Limiting Distribution of Quadratic Deviation of Estimators of Regression Curves --
5. Nonparametric Estimators of Components of a Convolution (S.N. Bernstein's Problem) --
5. Projection Type Nonparametric Estimation of Probability Density --
1. Consistency of Projection-Type Probability Density Estimator in the Norms of Spaces C and L2 --
2. Limiting Distribution of the Squared Norm of a Projection-Type Density Estimator --
Addendum Limiting Distribution of Quadratic Deviation for a Wide Class of Probability Density Estimators --
1. Limiting Distribution of Un --
2. Kernel Density Estimators / Rosenblatt-Parzen Estimators --
3. Projection Estimators of Probability Density / Chentsov Estimators --
4. Histogram --
5. Deviation of Kernel Estimators in the Sence of the Hellinger Distance --
References --
Author Index.
Series Title: Mathematics and its Applications (Soviet Series), 20.
Responsibility: by E.A. Nadaraya.

Abstract:

'Et moi ..., si. j'avail su comment en revenir. One service mathematics has rendered!be human race. It has put common sense back jc n'y scrais point a1U: where it belongs, on the topmost sbelf next Jules Verne to \be dusty canister labelled 'discarded non- TIle series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic bas rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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`... this book is a useful and significant addition on the lively topic of nonparametric density and regression curve estimation.' Royal Statistical Society, 154, 1991

 
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