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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