'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.
Inhaltsverzeichnis
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 theNorms 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.
