Nonparametric Estimation of Probability Densities and Regression Curves

ISBN-13: 9789401076678 / Angielski / Miękka / 2012 / 213 str.

Nadaraya

Opis

'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 e 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.

Recenzje

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

Spis treści

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.