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AuthorNadaraya, E. A. author
TitleNonparametric Estimation of Probability Densities and Regression Curves [electronic resource] / by E. A. Nadaraya
ImprintDordrecht : Springer Netherlands, 1989
Connect tohttp://dx.doi.org/10.1007/978-94-009-2583-0
Descript IX, 213 p. online resource

CONTENT

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 ofโ{128}{153} singularโ{128}{153} 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. Bernsteinโ{128}{153}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 Statistics Statistical Theory and Methods



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