Normal Approximation : New Results, Methods and Problems
Vladimir V. Senatov
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
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| Utgitt | Munchen : : De Gruyter Mouton, , 2011.
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| Omfang | 1 online resource (375 p.)
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| Opplysninger | Description based upon print version of record.. - ""Foreword""; ""Preface""; ""1 Introduction""; ""1.1 Formulation of the problem""; ""1.2 Historical aspects; Qualitative effects of transition from the one-dimensional case to multidimensional spaces""; ""1.3 On the contents of the book""; ""1.4 Some notation and definitions""; ""2 Elements of the theory of probability metrics""; ""2.1 Basic probability metrics""; ""2.2 On distinctions between probability metrics""; ""2.3 Special properties of probability metrics""; ""2.4 Relations between metrics""; ""2.5 Structure of the set of metrics""; ""2.6 Estimates in equivalent metrics"". - ""2.7 The Lévy-Prokhorov metrics Weak convergence""; ""2.8 Uniform metrics""; ""2.9 Metrics λ and Ï?""; ""2.10 Ideal metrics""; ""2.11 Extremal properties of L and Ï? metrics""; ""3 Method of characteristic functions; Berry-Esseen theorem""; ""3.1 Basic properties of characteristic functions""; ""3.2 Estimation of closeness of characteristic functions in CLT""; ""3.3 Berry-Esseen inequality""; ""3.4 Berry-Esseen theorem""; ""3.5 Modifications of Berry-Esseen theorem""; ""3.6 One remark about the method of characteristic functions in the multidimensional case"". - ""4 Method of compositions in the one-dimensional case""""4.1 Preliminary remarks""; ""4.2 Smoothing inequality""; ""4.3 Basic estimate""; ""4.4 Speculations""; ""4.5 One modification of the method of compositions""; ""4.6 Convergence rate estimate under the condition β2+Î? < â?ž, 0<Î?<1""; ""5 Method of compositions in the multidimensional case""; ""5.1 Base estimates""; ""5.2 Estimates under the condition Var(Pn, Î?) â??0""; ""6 Convergence rate estimates in weak metrics""; ""6.1 On a relation between estimates of the Lévy-Prokhorov metrics"". - ""6.2 Estimation of the metrics Ï€ through the metrics ζ""""6.3 Estimation of Ï€(Pn, Î?; G) in the space l2""; ""6.4 Estimation of Ï€(Ρn, Î?; G) and Ï€(Ρn, Î?; B) in the space Ek""; ""6.5 Estimation of Ï€(Ρn, Î?; B) in the space l2""; ""6.6 A remark on the estimates in the central limit theorem for weak metrics""; ""7 Estimation of uniform distances in l2""; ""7.1 Some remarks on the method to prove the estimates""; ""7.2 Additional notation""; ""7.3 Formulation and proof of the theorem""; ""8 Estimation of derivatives and measures"". - ""8.1 Derivatives of the functions Î?(rk(x) â€? Ï?)/Ï?) and η(rk(x) - Ï?)/Ï?)""""8.2 Derivatives of the normal law""; ""8.3 Estimates of the Pn-measure of the sets F(ε) and Î?(ε)""; ""8.4 On a bound in the space Ek""; ""9 Lower bounds for uniform metrics""; ""Conclusion""; ""Bibliography""; ""Index""
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| Emner | |
| Sjanger | |
| ISBN | 9067642924
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