Table Of ContentProbability, Statistics and Econometrics
Probability, Statistics
and Econometrics
Oliver Linton
UniversityofCambridge
UnitedKingdom
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Contents
LisotfF igures xiii
Aboutth eA uthor xv
Preface XVII
Acknowledgment xix
ParIt
ProbabialnidtD yi stribution
1. ProbabiTlhietoyr y
3
1.1I ntroduction
4
1.2D efinitoifPo rno bability
7
1.3S omeC ountiPnrgo blems
2.
ConditioPnraolb abialnidtI yn dependence
11
2.1C onditioPnraolb ability
12
2.2B ayeTsh eorem
14
2.3I ndependence
3.
RandomV ariablDeissr,ti butiFounn ctioannsd,
Densities
21
3.1R andomV ariables
23
3.2D istribuFtuinocnt ions
27
3.3Q uantile
31
3.4D ensiatnyd M assF unctions
4.
TransformaotfiR oannsd omV ariables
35
4.1D istribuotfiF ounnsc tioofna s R andomV ariable
40
4.2P robabiIlnitteyg Trraaln sform
VII
viiCio ntents
5.
The Expectation
5.1D efiniiont andP roperties 43
5.2A dditioMnoamle ntasn dC umulasn t 49
5.3A n InterpretoafEt xipoenc tatainodMn e dian 52
U i
6. Exampleosf nivarateD istributions
6.1P arametrFiacm ilioefsD istributions 55
6.1.1D iscrDeitset ributions 55
6.1.2C ontinuoDuiss tributions 58
7.
MultivarRianadtoem V ariables
7.1M ultivarDiisattrei bonust i 63
7.2C onditioDniaslt ribuatnidoI nnsd ependence 66
7.3C ovariance 69
7.4C onditioEnxaple ctaatnidot nh eR egressFiuonnc tion 72
7.5E xamples 81
7.6M ultivariate Transformations 85
7.6.1S omeS peciCaals eWsh ereq =1 andp = 2 87
7.6.2Co pula 90
8.
AsymptotTihce ory
8.1I nequalities 93
8.2N otioonfsC onvergence 96
8.3L awso fL argNeu mberasn dC LT 100
8.3.1G amblinMgo del 103
8.4S omeA dditionTaolo ls 105
9.
ExerciasnedsC omplements
ParIt I
Statistics
10.I ntroduction
10.1S ampliTnhego ry 135
10.2S amplSet atistics 136
10.2.P1r opertoifDe ess cripSttiavtei stics 138
10.2.E2x acPtr operties Stpot ehceNi ofrimca Dli stribution1 40
10.3S tatisPtriicnacli ples 142
10.3.S1o meI mportCaonntc epts 144
10.3.B2a yesiMaent hods 146
ContentIsX
11.E stimatTihoeno ry
11.1E stimatMieotnh ods 151
11.1.T1 heO riginMaelt hoodf M omentosr A nalogPyr iinpcle 151
11.1.M2 aximumL ikelihood 155
11. 1.3C omputation 160
11.2C omparisoonf E stimatoarnsd O ptimality 163
11.2.A1 symptotPirco perties 170
11.3R obustneasns dO theIrs suweist thh eM LE 172
12.H ypotheTseisst ing
12.1H ypotheses 175
12.2T estP rocedure 176
12.3L ikelihToeosdt s 181
12.4P oweor fT ests 18 4
12.4.1N eymanP earsOopnt imaTle sting 186
12.4.C2 onsisteonfTc eys tasn dL ocaPlo wer 189
12.4.N3 onparameTtersitci ng 193
12.5C riticisms oft heS tandaHrydp otheseistsni gT Approach 196
13.C onfindceeI ntervaanldSs e ts
13.1D efinitions 199
13.1.1G eneraLla rgSea mplSee tting 201
13.2L ikelihRoaotdi Coo nfidenIcnet erval 203
13.2.A1 BayesiIannt erval 208
13.3M ethodosf E valuatIinntge rvals 209
14.A sympottiTce stasn dt heB ootstrap
14.1S imulation Methods 211
14.2B ootstrap 212
14.2.S1 ubsampling 219
15.E xerciasnedsC omplements
ParItI I
Econometrics
16.L ineAalrg ebra
16.1M atrices 231
16.1.1L ni earS paces 236
16.1.2E igenvecatnodrE si genvalues 237
16.1.A3 pplciations 244
16.2S ystemosfL ineEaqru atioannsdP rojection 249
x Contents
17.
The LeasStq uarePsr ocedure
17.1 ProjectionA pproach 251
17.2P artiitoned Regression 255
17.3R estricLteeads t Squares 257
17.3.B1a ckfititnLi innge Raerg ression 259
17 .3.G2o odnesosf F it 261
18.
LineMaord el
18.1I ntroduction 263
18.2T heM odel 263
19.
StatistPircoaple rtoifte hse O LSE stimator
19.1P ropetreiso fO LS 267
19.1.A1l ternatEisvtei mators 271
19.2O ptimality 271
20.H ypotheTseisst ifnogrL ineaRre gression
20.1H ypothesoefsI nterest 277
20.2T esotf a SinglLei neaHry pothesis 278
20.3T esotf M ultipLlien eHayrp othesis 280
2004T esotf M ultpile LineaHry potheBsaisse odn F it 281
20.5L ikelihoodB aseTde sting 285
20.6B ayesian pApraoch 287
21.
OmissioofnR elevaVnatr iablIensc,l usoifoI nr relevant
VariablaensdM, o delS election
21.1O missioonfR elevaVnatr iables 289
21.2I nclusoifoI nr relevVaanrti ables/KnowolfPe adrgaem eters 291
21.3M odelS election 292
21.3.P1r oblemasn dI ssues 293
21.4L asso 294
22.A symptotPirco pertoifeO sL SE stimataonrdT est
Statistics
22.1T heL l.DC.as e 297
22.T2h e Non-Ll.CDa.s e 302
23.
GeneraliMzeetdh odo fM omentsa ndE xtremum
Estimators
23.1G eneraliMzeetdh odM oments 313
