Statistics for mathematicians: a rigorous first course
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Basel]
Birkhäuser
[2016]
|
| Schriftenreihe: | Compact textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xv, 177 Seiten Diagramme |
| ISBN: | 9783319283395 |
| ISSN: | 2296-4568 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents Regular Probability Models .................................................................... 1.1 Discrete Regular Models.................................................................. 1.2 Continuous Regular Models............................................................ 1.3 Exponential Families of Distributions.............................................. 1.4 Transforming Probability Models .................................................... 1.5 Model Selection and Exploratory Data Analysis............................. 1.5.1 Exploratory Data Analysis.................................................... 1 2 9 16 19 26 28 2 Sampling from Probability Distributions .............................................. 2.1 Sampling, Statistics and Sufficiency................................................. 2.2 Sampling from a Normal Distribution.............................................. 2.3 Sampling from an Exponential Family............................................. 2.4 Approximate Sampling Distributions .............................................. 2.4.1 Approximate Distributions for Sums.................................... 2.4.2 Approximate Distributions for Functions of Sums.............. 41 41 44 50 53 55 57 3 Point Estimation of Model Parameters.................................................. 3.1 Criteria for Comparing Estimators.................................................. 3.2 Fundamental Limitations to Estimation Accuracy........................... 3.3 Methods for Constructing Estimators .............................................. 3.3.1 The
Method of Maximum Likelihood.................................. 3.3.2 Maximum Likelihood in Exponential Families.................... 3.3.3 Large Sample Properties of Maximum Likelihood.............. 3.3.4 Other Estimation Methods.................................................... 3.4 Estimation Methods vs Estimators vs Estimates.............................. 61 62 64 68 68 75 76 86 92 4 Tests of Hypotheses for Model Parameters ........................................... 4.1 Test Functions and Error Types........................................................ 4.2 The Neyman-Pearson Framework.................................................... 4.3 Methods for Constructing Test Functions........................................ 4.3.1 Simple Case......................................................................... 4.3.2 Unilateral Case.................................................................... 4.3.3 Bilateral Case....................................................................... 4.4 The p -Value..................................................................................... 4.5 On Terminology: Accepting Versus Not Rejecting.......................... 95 96 100 102 103 109 113 124 128 1 xi
xii Contents Confidence Intervals for Model Parameters.......................................... 5.1 Confidence Intervals and Confidence Levels................................... 5.2 Pivots and Approximate Pivots....................................................... 5.2.1Approximate Pivotsin Exponential Families............................ 5.3 The Duality with Hypothesis Tests.................................................. 5.4 Optimality in Interval Estimation..................................................... 5.5 On Interpreting Confidence Intervals............................................... 131 132 136 139 141 145 148 Appendix......................................................................................................... A.l Probability Factsheet....................................................................... A.2 Taylor’s Formula and the Inverse Function Theorem...................... A.3 Two Concentration Inequalities....................................................... A.4 Monotonicity and Covariance.......................................................... A.5 Quantiles.......................................................................................... A.6 Moment Generating Functions......................................................... A.7 Continuous Mapping and Slutsky’s Theorem.................................. A.8 On the Proof of the Central Limit Theorem..................................... 151 151 158 159 160 160 163 169 173
Bibliography................................................................................................... 177 5
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| classification_rvk | SK 830 SK 850 |
| ctrlnum | (OCoLC)953180057 (DE-599)BVBBV043648587 |
| discipline | Mathematik |
| format | Book |
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| spelling | Panaretos, Victor M. 1982- Verfasser (DE-588)1089631340 aut Statistics for mathematicians a rigorous first course Victor M. Panaretos [Basel] Birkhäuser [2016] © 2016 xv, 177 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Compact textbooks in mathematics 2296-4568 Mathematical statistics Mathematik (DE-588)4037944-9 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s Mathematik (DE-588)4037944-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-28341-8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029062227&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Panaretos, Victor M. 1982- Statistics for mathematicians a rigorous first course Mathematical statistics Mathematik (DE-588)4037944-9 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Statistics for mathematicians a rigorous first course |
| title_auth | Statistics for mathematicians a rigorous first course |
| title_exact_search | Statistics for mathematicians a rigorous first course |
| title_full | Statistics for mathematicians a rigorous first course Victor M. Panaretos |
| title_fullStr | Statistics for mathematicians a rigorous first course Victor M. Panaretos |
| title_full_unstemmed | Statistics for mathematicians a rigorous first course Victor M. Panaretos |
| title_short | Statistics for mathematicians |
| title_sort | statistics for mathematicians a rigorous first course |
| title_sub | a rigorous first course |
| topic | Mathematical statistics Mathematik (DE-588)4037944-9 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical statistics Mathematik Statistik Lehrbuch |
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