Nonparametric estimation for a windowed line segment process:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1997
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract
121 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | II, 152 S. graph. Darst. |
| ISBN: | 9061964741 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011543408 | ||
| 003 | DE-604 | ||
| 005 | 19971114 | ||
| 007 | t | ||
| 008 | 970922s1997 d||| |||| 00||| eng d | ||
| 020 | |a 9061964741 |9 90-6196-474-1 | ||
| 035 | |a (OCoLC)37341766 | ||
| 035 | |a (DE-599)BVBBV011543408 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-384 |a DE-188 | ||
| 050 | 0 | |a QA276.8 | |
| 082 | 0 | |a 519.5 |2 20 | |
| 084 | |a SK 835 |0 (DE-625)143260: |2 rvk | ||
| 084 | |a MAT 626f |2 stub | ||
| 084 | |a MAT 634f |2 stub | ||
| 100 | 1 | |a Wijers, Bart J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonparametric estimation for a windowed line segment process |c B. J. Wijers |
| 264 | 1 | |a Amsterdam |c 1997 | |
| 300 | |a II, 152 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |v 121 | |
| 650 | 7 | |a Estimation de paramètres |2 ram | |
| 650 | 7 | |a Lijnstukken |2 gtt | |
| 650 | 7 | |a Non-parametrische statistiek |2 gtt | |
| 650 | 7 | |a Schattingen |2 gtt | |
| 650 | 7 | |a Waarnemingen |2 gtt | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Parameter estimation | |
| 650 | 0 | 7 | |a Nichtparametrische Schätzung |0 (DE-588)4203980-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Strecke |0 (DE-588)4183620-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtparametrische Schätzung |0 (DE-588)4203980-0 |D s |
| 689 | 0 | 1 | |a Strecke |0 (DE-588)4183620-0 |D s |
| 689 | 0 | 2 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |v 121 |w (DE-604)BV001902011 |9 121 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007770980 | ||
Datensatz im Suchindex
| _version_ | 1804126066736889856 |
|---|---|
| adam_text | Contents
Introduction 1
1 The models 5
1.1 The one dimensional line segment process 5
1.1.1 The hospital model 5
1.1.2 Missing data problem 7
1.1.3 Identification 11
1.1.4 The likelihood and the definition of the NPMLE 19
1.1.5 Existence and uniqueness of the NPMLE 20
1.1.6 EM algorithin and self consistency equations 23
1.1.7 The sieved NPMLE 25
1.2 The two dimensional line segment process 27
1.2.1 The model 27
1.2.2 The window W is a circle 31
1.2.3 Identification in the case W is a circle 38
1.2.4 The likelihood, the NPMLE, in the case W is a circle 39
1.2.5 W is an arbitrary convex window 40
1.2.6 The likelihood, the NPMLE, in the case W is arbitrary convex 44
2 Consistency 47
2.1 General idea 48
2.2 Consistency in the one dimensional case 49
2.2.1 Proof of consistency in the one dimensional case 54
2.2.2 Three propositions and a lemma 58
2.2.3 Proof of two propositions of chapter 1 65
2.3 Consistency in the two dimensional circle case 66
2.3.1 Proof of consistency in the two dimensional circle case 68
3 Efficiency 75
3.1 General notion of efficiency 75
3.1.1 Donsker class 75
3.1.2 Efficiency theory 77
3.2 Efficiency theorem for an NPMLE 80
3.3 Efficiency of NPMLE of linear parameters in convex models 82
3.4 The assumptions 87
ii
3.5 The parameters to be estimated 88
3.5.1 The parameter Mi(iV) = Z(t) 89
3.5.2 The parameter t?2(iV) = Z 90
3.5.3 Efficiency of (Zn,Zn) implies efficiency of (#„,£„) 91
3.6 The score operator Ay and the information operator Iv 92
3.7 Calculation of/yl(X( ~ 2(i)) 93
3.7.1 Invertibility of Iv(ht)(x) = x«(*) for x 2R 93
3.7.2 Invertibilityof 7v(A,)(i) = Xi(i)for i£ [0,2i?) 96
3.8 The Donsker class condition 102
3.8.1 ||rv||v and ||«v||v are bounded 103
3.8.2 The boundedness of ||(7 Bv) /IL 105
3.8.3 Sv and Tv are bounded operators 108
3.8.4 The score operator A is a bounded operator w.r.t. || • 0,, norm .... 109
3.8.5 The determinants Dy and Qv are continuous in V Ill
3.8.6 Verification of the Donsker class condition 115
3.9 The || • Hp^ convergence conditions 116
3.9.1 Calculating I(Z,t) I(Zn,t) 117
3.9.2 Verification of the || • Hpy convergence condition 120
3.10 The determinant Qv / 0 and assumption I 121
3.10.1 Some remarks about the determinant Qv 121
3.10.2 The assumption g(2R) 0 and d(2R,2R) 0 121
3.11 Calculation of Iyl(( Z) 124
3.12 Efficiency proof for the one dimensional case 127
3.12.1 The parameters {W, W) to be estimated 128
3.12.2 Calculation of /^(k, W(ij) 130
3.12.3 One dimensional case versus two dimensional case 133
4 Open problems 135
4.1 Suggestion to solve the r and 2R singularity 135
4.1.1 Regrouping in the one dimensional case 136
4.1.2 Regrouping in the two dimensional circle case 142
4.2 Non homogeneous Poisson point process 142
4.2.1 A(t) is unknown if t 0 and 0 otherwise 143
4.3 Non convexity of the window W 144
4.4 A conjecture: the determinant Qv 1 145
Bibliography 147
Index 151
|
| any_adam_object | 1 |
| author | Wijers, Bart J. |
| author_facet | Wijers, Bart J. |
| author_role | aut |
| author_sort | Wijers, Bart J. |
| author_variant | b j w bj bjw |
| building | Verbundindex |
| bvnumber | BV011543408 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.8 |
| callnumber-search | QA276.8 |
| callnumber-sort | QA 3276.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 835 |
| classification_tum | MAT 626f MAT 634f |
| ctrlnum | (OCoLC)37341766 (DE-599)BVBBV011543408 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02013nam a2200517 cb4500</leader><controlfield tag="001">BV011543408</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19971114 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">970922s1997 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9061964741</subfield><subfield code="9">90-6196-474-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)37341766</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011543408</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA276.8</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 835</subfield><subfield code="0">(DE-625)143260:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 626f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 634f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wijers, Bart J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonparametric estimation for a windowed line segment process</subfield><subfield code="c">B. J. Wijers</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">II, 152 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract</subfield><subfield code="v">121</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Estimation de paramètres</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lijnstukken</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Non-parametrische statistiek</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Schattingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Waarnemingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Parameter estimation</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtparametrische Schätzung</subfield><subfield code="0">(DE-588)4203980-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Strecke</subfield><subfield code="0">(DE-588)4183620-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtparametrische Schätzung</subfield><subfield code="0">(DE-588)4203980-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Strecke</subfield><subfield code="0">(DE-588)4183620-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract</subfield><subfield code="v">121</subfield><subfield code="w">(DE-604)BV001902011</subfield><subfield code="9">121</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007770980</subfield></datafield></record></collection> |
| id | DE-604.BV011543408 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:33Z |
| institution | BVB |
| isbn | 9061964741 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007770980 |
| oclc_num | 37341766 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-188 |
| physical | II, 152 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| record_format | marc |
| series | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| spelling | Wijers, Bart J. Verfasser aut Nonparametric estimation for a windowed line segment process B. J. Wijers Amsterdam 1997 II, 152 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 121 Estimation de paramètres ram Lijnstukken gtt Non-parametrische statistiek gtt Schattingen gtt Waarnemingen gtt Distribution (Probability theory) Parameter estimation Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Strecke (DE-588)4183620-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Nichtparametrische Schätzung (DE-588)4203980-0 s Strecke (DE-588)4183620-0 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 121 (DE-604)BV001902011 121 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wijers, Bart J. Nonparametric estimation for a windowed line segment process Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract Estimation de paramètres ram Lijnstukken gtt Non-parametrische statistiek gtt Schattingen gtt Waarnemingen gtt Distribution (Probability theory) Parameter estimation Nichtparametrische Schätzung (DE-588)4203980-0 gnd Strecke (DE-588)4183620-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4203980-0 (DE-588)4183620-0 (DE-588)4057630-9 |
| title | Nonparametric estimation for a windowed line segment process |
| title_auth | Nonparametric estimation for a windowed line segment process |
| title_exact_search | Nonparametric estimation for a windowed line segment process |
| title_full | Nonparametric estimation for a windowed line segment process B. J. Wijers |
| title_fullStr | Nonparametric estimation for a windowed line segment process B. J. Wijers |
| title_full_unstemmed | Nonparametric estimation for a windowed line segment process B. J. Wijers |
| title_short | Nonparametric estimation for a windowed line segment process |
| title_sort | nonparametric estimation for a windowed line segment process |
| topic | Estimation de paramètres ram Lijnstukken gtt Non-parametrische statistiek gtt Schattingen gtt Waarnemingen gtt Distribution (Probability theory) Parameter estimation Nichtparametrische Schätzung (DE-588)4203980-0 gnd Strecke (DE-588)4183620-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Estimation de paramètres Lijnstukken Non-parametrische statistiek Schattingen Waarnemingen Distribution (Probability theory) Parameter estimation Nichtparametrische Schätzung Strecke Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT wijersbartj nonparametricestimationforawindowedlinesegmentprocess |