Download RANDOM PROCESSES AND TIME SERIES CONFERENCE

RANDOMPROCESSESANDTIMESERIESCONFERENCE:THEORYANDAPPLICATIONS
October21-23,2016
TITLESANDABSTRACTSOFTALKS
Alltalks,exceptpossiblyforthosebyRobertEngleandCatherineConstablewillbeintheNatural
SciencesBuilding(NSB)AuditoriumatUCSanDiego.
(FordirectionstotheNaturalSciencesBuildinggoto
http://physicalsciences.ucsd.edu/about/map.html.
Theauditoriumisonthegroundfloor.)
FRIDAY,OCTOBER21,2016
1-1.30PM:Registrationcheckin
1.30PM:OPENING
1.45-2.30PM:MagdaPeligrad,UniversityofCincinnati
Randomfields,spectraldensityandempiricalspectraldistribution
Thetalkwillbeconcernedwithstationaryrandomfields,theirspectraldensityandlimitingbehavior.
Thetheoryofstationaryrandomfieldsissheddinglightonthelimitingspectraltheoryoflargerandom
matrices,i.e.thedistributionoftheeigenvaluesasthesizeofthematrixgoestoinfinity.Weshallpoint
outarelationshipbetweenthelimitingspectraldistributionofrandommatriceswithentriesselected
fromastationaryrandomfieldanditsspectraldensity.ThetalkwillbebasedonjointpaperswithM.
Banna,F.Merlevède,M.LifshitsandC.Peligrad.
2.30-3.15PM:RichardBradley,IndianaUniversity
OnmixingpropertiesofsomeINARmodels
Intimeseriesanalysisof(nonnegativeinteger-valued)
``countdata'',onesometimesuses``integervalued
autoregressive''(INAR)models,avariantoftheoriginalautoregressivemodelsofclassicaltime
seriesanalysis.
TheINARmodelsoforder1with``Poissoninnovations''
satisfy(withexponentialmixing
rate)the``interlaced
rho-mixing''condition(thestrongervariantoftheusual
rho-mixingconditionin
whichthetwoindexsetsare
allowedtobe``interlaced''insteadofbeingrestricted
to``past''and
``future'').Thatwasshownin
R.C.Bradley,ZapiskiNauchnyhSeminarovPOMI441(2015)56-72,and
willbeexplainedinthistalk.Earlier,
S.SchweerandC.H.Weiss,Comput.Statist.DataAnal.77(2014)
267-284,
hadalreadyshownthatthosemodels(aswellassomeothercloselyrelatedones)satisfy
absoluteregularitywithexponentialmixingrate.
3.15-4PM:Postersandcoffeebreak(NSBAtrium)
4-4.45PM:MuradTaqqu,BostonUniversity
PropertiesandnumericalevaluationoftheRosenblattdistribution
WestudyvariousdistributionalpropertiesoftheRosenblattdistribution.Weshowhowits
expansionusingcenteredchi-squaredrandomvariablesallowsustocomputecumulants,
moments,thecoefficientsoftheexpansionandthedensityandcumulativedistributionfunctions
oftheRosenblattdistributionwithahighdegreeofprecision.
ThisisjointworkwithMarkVeillette.
5-6.15PM:
MurrayandAdylinRosenblattEndowedLectureinAppliedMathematics
Speaker:RobertEngle,NewYorkUniversity
Title:DynamicConditionalBeta
Abstract:
DynamicConditionalBeta(DCB)isanapproachtoestimatingregressionswithtimevaryingparameters.
Theconditionalcovariancematricesoftheexogenousanddependentvariableforeachtimeperiodare
usedtoformulatethedynamicbeta.Jointestimationofthecovariancematricesandotherregression
parametersisdeveloped.Testsofthehypothesisthatbetasareconstantarenon-nestedtestsand
severalapproachesaredevelopedincludinganovelnestedmodel.Themethodologyisappliedto
industrymultifactorassetpricingandtoglobalsystemicriskestimationwithnon-synchronousprices.
Receptiontofollowwithpostersession.
SATURDAY,OCTOBER22,2016
9.30-10.15AM:PhilipStark,UniversityofCalifornia,Berkeley
SimpleRandomSamplingisnotthatSimple
Asimplerandomsample(SRS)ofsizekfromapopulationofsizenisasampledrawnatrandominsuch
awaythateverysubsetofkofthenitemsisequallylikelytobeselected.Thetheoryofinferencefrom
SRSsisfundamentalinstatistics;manytechniquesandformulaeassumethatthedataareanSRS,
includingparametricandnonparametricmethods,suchaspermutationtests.TrueSRSsarerare;in
practice,samplesaredrawnusingpseudo-randomnumbergenerators(PRNGs)andalgorithmsthatmap
asetofpseudo-randomnumbersintoasubsetofthepopulation.Moststatisticianstakeforgranted
thattheirsoftwarepackage"doestherightthing,"producingsamplesthatcanbetreatedasiftheyare
SRSs.Infact,thePRNGalgorithmandthealgorithmfordrawingsamplesusingthePRNGmatter
enormously.Somewidelyusedmethodsareparticularlybad.Evenformodestvaluesofnandk,the
methodscannotgenerateallsubsetsofsizek;thesubsetstheydogeneratemaynothaveequal
frequencies;andtheyarenumericallyinefficient.Forinstance,themethodusedbyRdoesnoteven
haveequalfirst-orderselectionprobabilities;for"bigdata"withn=10^9,thechancethatasingleitem
willbeinthesamplecanvarybyabout25%acrossitems.Relyingoncommonalgorithmsforgenerating
SRSsfromstandardPRNGsintroducesbiasintootherwiseunbiasedestimatorsandmakestheusual
uncertaintycalculationsinvalid.Thesituationforsamplingwithreplacement--thefoundationforthe
bootstrap--isworsestill.
ThisisjointworkwithKellieOttoboni,UCBerkeley,andRonaldL.Rivest,MIT.
10.15-11AM:WeiBiaoWu,UniversityofChicago
Aunifiedasymptotictheoryforstationaryprocesses
MotivatedbyRosenblatt(1960),wepresentasystematicasymptotictheoryforstatisticsofstationary
timeseries.Inparticular,weconsiderpropertiesofsamplemeans,samplecovariancefunctions,
covariancematrixestimates,periodograms,spectraldensityestimates,kerneldensityandregression
estimatesoflinearandnonlinearprocesses.Theasymptotictheoryisbuiltuponfunctionaland
predictivedependencemeasures,anewmeasureofdependencewhichisbasedonnonlinearsystem
theory.Ourdependencemeasuresareparticularlyusefulfordealingwithcomplicatedstatisticsoftime
seriessuchaseigenvaluesofsamplecovariancematricesandmaximumdeviationsofnonparametric
curveestimates,generalizingtheseminalworkBickelandRosenblatt(1973).
11-11.30AM:CoffeeBreak
11.30-12.15:Keh-ShinLii,UniversityofCalifornia,Riverside
Modelingandpredictingnon-stationarypointprocesses
Weconsideraclassofpointprocesseswithperiodicoralmostperiodicintensityfunctions.These
modelsdealwiththeoccurrenceofeventswhichareunequallyspacedandhaveapatternofperiodicity
oralmostperiodicity,suchasstocktransactionsandaccidents.Wemodeltherateofoccurrenceof
suchmodelsasasumofsinusoidalfunctionsplusabaseline.Problemsofconsistentestimationsofthe
frequencies,phasesandamplitudesarediscussed.Issueofpredictionareexplored.PoissonandnonPoissoncasesareconsidered.Simulationandrealdataexamplesareusedtoillustratetheresults.
SATURDAYAFTERNOON,OCTOBER22,2016
12.15-1.45PM:LUNCHONYOUROWN
1.45-3PM:
MurrayandAdylinRosenblattEndowedLectureinAppliedMathematics
Speaker:CatherineConstable,InstituteofGeophysicsandPlanetaryPhysics
ScrippsInstitutionofOceanography,UniversityofCalifornia,SanDiego
Title:Earth'sMagneticField:RandomReversals,StochasticModels,andPhysical
Interpretations
Directobservationsofthemoderngeomagneticfieldenableustounderstanditsroleinprotectingus
fromthedepredationsofthesolarwindandassociatedspaceweather,whilepaleomagneticstudies
providegeologicalevidencethatthefieldisintimatelylinkedwiththehistoryandthermalevolutionof
ourplanet.Inthepastthemagneticfieldhasreversedpolaritymanytimes:suchreversalsoccurwhen
itsoverallstrengthdecays,andtherearedeparturesfromtheusualspatialstructurewhichatEarth's
surfacepredominantlyresemblesthatofanaxiallyaligneddipole.Reversalsareoneelementofa
continuumofgeomagneticfieldbehaviorwhichalsoincludesgeomagneticexcursions(oftenviewedas
unsuccessfulreversals),andpaleosecularvariation.Thefragmentaryandnoisynatureofthegeological
recordcombinedwithdistancefromthefield'ssourceinEarth'sliquidoutercoreprovidealimited
view,butonethathasbeenpartiallycharacterizedbytimeseriesanalysis,anddevelopmentof
stochasticmodelsdescribingthevariability.Analysesofchangesinthedipolemomenthaverevealed
distinctstatisticalcharacteristicsassociatedwithgrowthanddecayoffieldstrengthinsomefrequency
ranges.Paleomagneticstudiesarecomplementedbycomputationallychallengingnumerical
simulationsofgeomagneticfieldvariations.Accesstodetailswithinthenumericalmodelallowthe
evolutionoflargescalephysicalprocessestobestudieddirectly,anditisofgreatinteresttodetermine
whetherthesecomputationalresultshaveEarth-likeproperties.Theparameterregimeaccessibleto
thesesimulationsisfarfromideal,buttheiradequacycanbeassessedandfuturedevelopmentguided
bycomparisonsoftheirstatisticalpropertieswithrobustresultsfrompaleomagneticobservations.
Progressingeomagneticstudieshasbeengreatlyfacilitatedbytheapplicationofstatisticalmethods
relatedtostochasticprocessesandtimeseriesanalysis,andthereremainssignificantscopefor
continuedimprovementinourunderstanding.Thisislikelytoproveparticularlyimportantfor
understandingthescenariosthatcanleadtogeomagneticreversals.
3-3.30PM:CoffeeBreak
(SEENEXTPAGEFORTWOMOREAFTERNOONTALKS)
SATURDAY,OCTOBER22,2016(CONTINUED)
3.30-4.15PM:RichardOlshen,StanfordUniversity
MurrayRosenblatt,UCSD,andClonality
Mypresentationhasthreesomewhatdistinctparts,withthefirsttwo,MurrayRosenblattandUCSD,
morecloselyrelatedthaneitheristothethird:mycurrentstudieswithothersoftheestimationof
functionalsofaprobabilityvectorthatsummarizesfrequenciesofso-calledV(D)Jrearrangementsof
particulartypesofBcellsandTcellsoftheadaptivehumanimmunesystem.Datacomefromassumed
independentandinonesenseidenticallydistributed`replicates,'andconsistofcounts.Oneimportant
componentofthehumanimmunesystemisthesumofsquaresofentriesoftheprobabilityvectorthat
istermed`clonality.'The``why''andthe``how''willbeexplained.
4.15-5PM:AnthonyGamst,UniversityofCalifornia,SanDiego
ModelSelectionandAdaptiveEstimation
MurrayRosenblattmadefundamentalcontributionstothetheoryofnon-parametriccurveestimation,
startingwithhisseminal1956paperondensityestimation,whichshowedthatunbiaseddensity
estimatesdonotexistandinspiredmuchofthesubsequentworkinnon-parametricestimation.These
andrelatedtechniqueshavebecometheworkhorsesofmodernmachinelearning.Strikingtheproper
balancebetweenapproximationandestimationerror--biasandvariance--isthekeytoproducing
optimalestimators.Achievingthisbalanceismodelselection'sgoal.Oneisfacedwithchoices
concerningwhichvariablestoincludeinthemodel,theextentoflocalaveragingtouse,andthedegree
ofinteractiontoallowbetweentheincludedvariables,amongothers.Andonewouldliketohavea
techniquewhichmakesthebestchoicesfor--thatis,adaptsto--theproblemathand,notjustthebest
choices,onaverage,foraclassofproblems.Allmachinelearningalgorithms,includingrelatively
impenetrabletoolslikedeepneuralnetworks,haveparameterswhichcontrolsomeorallofthese
features--controllingtheextenttowhichagivenmodelfitsthetrainingdatamoreorlesscloselythan
optimal.Wewilldiscusssomerecentworkinselectingmodelswhichareadaptiveandfinite-sample
optimal.
5.30PM:Dinner,FacultyClub,UCSanDiego
(advancepurchaseofdinnerticketsisrequired)
MC:KarenMesser,DivisionofBiostatisticsandBioinformatics,UCSanDiego
SUNDAY,OCTOBER23,2016
9.30-10.15AM:RichardDavis,ColumbiaUniversity
NoncausalVectorARProcesseswithApplicationtoEconomicTimeSeries
FollowinguponRosenblatt’sextensiveworkonnon-minimumphasemodeling(seeRosenblatt(2000),
“GaussianandNon-GaussianLinearTimeSeriesandRandomFields”,Springer),weconsiderinference
proceduresforpossiblynoncasualvectorautoregressions(AR).Inferenceproceduresfornoncausal
autoregressiveunivariatemodelshavebeenwellstudiedandappliedinavarietyofapplicationsfrom
environmentaltofinancial.Forsuchprocesses,theobservationsattimetmaydependonbothpastand
futureshocksinthesystem.Inthistalk,wewillconsiderextensionsoftheunivariatenoncausalAR
modelstothevectorAR(VAR)case.Theextensionpresentsseveralinterestingchallengessinceevena
first-orderVARcanpossessbothcausalandnoncausalcomponents.Assuminganon-Gaussian
distributionforthenoise,weshowhowtocomputeanapproximationtothelikelihoodfunction.Under
suitableconditions,itisshownthatthemaximumlikelihoodestimator(MLE)ofthevectorofAR
parametersisasymptoticallynormal.Theestimationprocedureisillustratedwithasimulationstudyfor
aVAR(1)processandwithtwomacro-economictimeseries.Semiparametricattemptsatestimationfor
thesemodelswillalsobementioned.
ThisisjointworkwithLiSongandJingZhang.
10.15-11AM:DimitrisPolitis,UniversityofCalifornia,SanDiego
FromNonparametricstoModel-Free:atimeseriestimeline
11-11.30AM:CoffeeBreak
11.30AM-12.15PM:LarryGoldstein,UniversityofSouthernCalifornia
NormalApproximationforRecoveryofStructuredUnknownsinHigh
Dimension:SteiningtheSteinerformula
(Seenextpageforabstract)
Normal approximation for recovery of structured
unknowns in high dimension: Steining the Steiner
formula
Larry Goldstein, University of Southern California
Abstract
Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications. In particular, the discrete probability distribution L(VC )
given by the sequence v0 , . . . , vd of conic intrinsic volumes of a closed convex cone C in Rd
summarizes key information about the success of convex programs used to solve for sparse
vectors, and other structured unknowns such as low rank matrices, in high dimensional
regularized inverse problems. Concentration of VC about its mean implies the existence of
phase transitions for the probability of recovery of the structured unknown as a function
of the number of observations. Additional information about the probability of recovery
success is provided by a normal approximation for VC . Such central limit theorems can be
shown by first considering the squared length GC of the projection of a standard Gaussian
vector on the cone C. Applying a second order Poincaré inequality, proved using Stein’s
method, then produces a non-asymptotic total variation bound to the normal for L(GC ).
A conic version of the classical Steiner formula in convex geometry translates finite sample
bounds and a normal limit for GC to that for VC .
Joint with Ivan Nourdin and Giovanni Peccati. http://arxiv.org/abs/1411.6265