عنوان

Nonparametric Estimation of Probability Densities and Regression Curves

9400925832

9789400925830

b592906

Nonparametric Estimation of Probability Densities and Regression Curves

[Book]

by E.A. Nadaraya.

Dordrecht

Springer Netherlands

1989

(IX, 213 pages)

Mathematics and its Applications (Soviet Series), 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 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.

Statistics.

by E.A. Nadaraya.

E A Nadaraya

[Book]

Y