{"title":"Mixingale Estimation Function for SPDEs with Random Sampling","authors":"J. Bishwal","doi":"10.28924/ada/stat.2.3","DOIUrl":null,"url":null,"abstract":"We study the mixingale estimation function estimator of the drift parameter in the stochastic partial differential equation when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we substitute this estimate in the estimation function to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the mixingale estimation function estimator.","PeriodicalId":153849,"journal":{"name":"European Journal of Statistics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28924/ada/stat.2.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We study the mixingale estimation function estimator of the drift parameter in the stochastic partial differential equation when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we substitute this estimate in the estimation function to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the mixingale estimation function estimator.
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