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The Problem of Estimating Dependences from
The Problem of Interpreting Results of Indirect Experiments
The Accuracy of Estimating Dependences on the Basis
97 other sections not shown
aemp algorithms approximation arbitrary assertion belonging bound Chapter class of densities class of functions complete sample compute consider construct convergence of frequencies covariance matrix cumulative distribution function decision rules F(x defined Denote density P(x determined deviation e-net emp(a empirical data empirical risk equality equivalence classes errors estimating dependences expected risk fulfilled function F(x hyperplane ill-posed problems indicator functions inequality Laplace distribution least-squares method lemma linear decision rules loss function mathematical expectation matrix means measure method of minimizing method of structural metric minimize the functional minimizes the empirical minimizing the expected normal distribution number of elements obtain operator equation parametric statistics pattern recognition polynomial prior information probability density problem of estimating problem of pattern Proof quantity random variable rate of uniform regression estimation right-hand side Section solution solving splines structural minimization structural risk minimization subdivided Theorem training sequence unbiased estimator uniform convergence utilize valid variance