指数型分布族中矩估计的序贯置信区间

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1、安徽大学硕士学位论文指数型分布族中矩估计的序贯置信区间姓名：陈思宝申请学位级别：硕士专业：数理统计指导教师：陈桂景;钱能生2003.5.12摘要本文主要讨论未知参数基于lE焦苴的雹基至垡臣塑的问题。参数估计的序贯方法自1965年Y．S．ChowllI研究一般总体均值u的序贯置信程序后而出现了一个崭新的发展局面。不少学者把这序贯方法应用到不同的模型中和不同的参数估计上，并指出其序贯估计的一些渐近性质，诸如：渐近相合性P(O∈1。)一口，渐近有效．EN(．d)---}1。n(a)最近，A．Dmitrienko(2000)【51

2、在构造极大似然估计的序贯置信区域时，提出了一个新的渐近性质：未知代价的有界性(boundedcostofignorance)，即脚(EⅣ(d)一n(d))

3、贯置信区间程序，着重算出它们极限分布中的相关渐近方差。最后指出，由定理的证明可知，上述矩估计序贯置信程序的渐近性质不受指数型分布族的限制，但要求一定的高阶矩有限。AbstractThispaperisconcernedwiththesequentialconfidenceintervalsforunknownparametersbasedonmomentestimates．ThesequentialmethodofintervalestimatesofparametersiScominguptoanewdevelopmen

4、tSinceY．S．Chowf5jconstruetedtheprogramofsequentialconfidenceintervalsforthemeanin1965．ManyascholarappliedthissequentialmethodtodifferentmodelSandtodifferentparametriceatimations．TheyalSOpointedoutsomeasymptoticpropertiesofthesequentialestimation，suchasasymptoticco

5、nsistency，thatisP(e∈IⅣ)oa，andasymptoticefficiency,thatis型_1．n(a)Recently,whenA．Dmitrienko(2000)嘲constructedthesequentialconfidenceregionsformaximum1ikelihoodestimates，theyputforwardanewasymptoticproperty：boundedCostofignorance，thatiS戮(群(矗)一《蠢))<∞·It'sanasymptoticp

6、ropertywhichisworthyofconsideration·Here,wewonderwhetherthoseasymptoticpropertiesarestilltruebasedonmomentestimates，whichhavebeenprovedtobetrueunderthemethodofmaximumlikelihoodestimatesandothermethods。Sowemainlydothefollowingworks：Firstly，werestrictthepopulationdi

7、slributioninthefamilyofexponentialdistributions，constructtheprogramofsequentialconfidenceintervalsfortheone·dimensionedfunctionofunknownparameterswithgeneralform，andacquireitssomeasymptoticproperties,such矗sasymptoticconsistency,asymptoticefficiencyandboundedcostof

8、ignorance．SecondlMweconstructthesequentialconfidenceintervalsforthecommonnumbercharacters：coefficientofvariation，skewnessandktlrtosis，stressingOilcomput