ABSTRACT

AnalogouslytoTheorem7.1wehaveforbothbootstrapsampling schemesforM-typeestimators:

THEOREM7.3.(Localchanges) (i)LetassumptionsofTheorem5.2besatisfied.Then,asn----+oo,

sup{P*(b,;(1j;)(1ii*M(77)- 1i1M(77))::;x) xER1

(7.9)

whereJDn},,fulfilsEq.(7.3)and611(1/;)=es,ll(rJ)- O,;,,t(,)withe,,,,t(IJ) andB,1,,t(,1)beingM-estimatorsbasedonY1,•.•,Y,1,11 (,1)and Y,;, 11 (,J)+I,...,Y11 ,respectively.D

ThisSectionisdevotedtotheapplicationstotwodatasets(Niledata andKlementinumdata)andalsototheresultsofasimulationstudythat checkstheperformanceoftheproposedmethodsforfinitesamplesituation.

Niledata Thisdatasetisprobablyoneofthemostfrequentlyusedinthegivensetup, fordetailssee,e.g.,Cobb(1978)orHinkleyandSchechtmann(1987).The data,i.e.theannualflowsintheriverNileatAswanduringtheyears18711970areshowninFig.I.