Nonparametric Estimation of Probability Densities and Regression Curves: Mathematics and its Applications, cartea 20

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.

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