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Record Nr. |
UNINA9910559398903321 |
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Autore |
Jiang Jiming |
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Titolo |
Large sample techniques for statistics / / Jiming Jiang |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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9783030916954 |
9783030916947 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (689 pages) |
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Collana |
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Springer Texts in Statistics |
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Disciplina |
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Soggetti |
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Mathematical statistics |
Sampling (Statistics) |
Mostreig (Estadística) |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- 1 The ε-δ Arguments -- 1.1 Introduction -- 1.2 Getting used to the ε-δ arguments -- 1.3 More examples -- 1.4 Case study: Consistency of MLE in the i.i.d. case -- 1.5 Some useful results -- 1.5.1 Infinite sequence -- 1.5.2 Infinite series -- 1.5.3 Topology -- 1.5.4 Continuity, differentiation, and integration -- 1.6 Exercises -- 2 Modes of Convergence -- 2.1 Introduction -- 2.2 Convergence in probability -- 2.3 Almost sure convergence -- 2.4 Convergence in distribution -- 2.5 Lp convergence and related topics -- 2.6 Case study: χ2-test -- 2.7 Summary and additional results -- 2.8 Exercises -- 3 Big O, Small o, and the Unspecified c -- 3.1 Introduction -- 3.2 Big O and small o for sequences and functions -- 3.3 Big O and small o for vectors and matrices -- 3.4 Big O and small o for random quantities -- 3.5 The unspecified c and other similar methods -- 3.6 Case study: The baseball problem -- 3.7 Case study: Likelihood ratio for a clustering problem -- 3.8 Exercises -- 4 Asymptotic Expansions -- 4.1 Introduction -- 4.2 Taylor expansion -- 4.3 Edgeworth expansion -- method of formal derivation -- 4.4 Other related expansions -- 4.4.1 Fourier series expansion -- 4.4.2 Cornish-Fisher expansion -- 4.4.3 |
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