{"title":"Simple Estimators of the Mixing Proportion in a Semi-Parametric Mixture with Known Component.","authors":"Fadoua Balabdaoui, Harald Besdziek","doi":"10.1007/s13171-025-00421-w","DOIUrl":"https://doi.org/10.1007/s13171-025-00421-w","url":null,"abstract":"<p><p>In this paper, we consider the problem of estimating a mixture of a background and signal component. The background distribution is fully known, while the signal distribution needs to be estimated along with the mixing proportion. We treat the special case where the support of the signal distribution is strictly included in that of the background. We show how this assumption can be accounted for in the estimation procedure to obtain a parametric rate of convergence for estimating the mixing proportion. In the case where the signal distribution admits a monotone, a monotone and convex or a log-concave density with respect to Lebesgue measure, we construct estimators that are based on the well-known shape-constrained approaches adapted for each one of these cases. Simulations are presented to illustrate the obtained theoretical results. We also showcase our methodology using prostate cancer data.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s13171-025-00421-w.</p>","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":"88 1","pages":"80-135"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12967557/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147391284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite Population Survey Sampling: An Unapologetic Bayesian Perspective.","authors":"Sudipto Banerjee","doi":"10.1007/s13171-024-00348-8","DOIUrl":"10.1007/s13171-024-00348-8","url":null,"abstract":"<p><p>This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical models, including some that yield design-based Horvitz-Thompson estimators, the article proceeds to introduce dependence in finite populations and sets out inferential frameworks for ignorable and nonignorable responses. Multivariate dependencies using graphical models and spatial processes are discussed and some salient features of two recent analyses for spatial finite populations are presented.</p>","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":"86 Suppl 1","pages":"95-124"},"PeriodicalIF":0.5,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12396637/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144973672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global-Local Shrinkage Priors for Asymptotic Point and Interval Estimation of Normal Means under Sparsity","authors":"Zikun Qin, Malay Ghosh","doi":"10.1007/s13171-023-00315-9","DOIUrl":"https://doi.org/10.1007/s13171-023-00315-9","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46014710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quadratic Prediction of Time Series via Auto-Cumulants","authors":"T. McElroy, Dhrubajyoti Ghosh, Soumendra Lahiri","doi":"10.1007/s13171-023-00326-6","DOIUrl":"https://doi.org/10.1007/s13171-023-00326-6","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46331043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exponential Bounds and Convergence Rates of Sieve Estimators for Functional Autoregressive Processes","authors":"Nesrine Kara Terki, T. Mourid","doi":"10.1007/s13171-023-00322-w","DOIUrl":"https://doi.org/10.1007/s13171-023-00322-w","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45990969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ting-Fung Ma, Juan Francisco Mandujano Reyes, Jun Zhu
{"title":"M-estimators for Models with a Mix of Discrete and Continuous Parameters","authors":"Ting-Fung Ma, Juan Francisco Mandujano Reyes, Jun Zhu","doi":"10.1007/s13171-023-00317-7","DOIUrl":"https://doi.org/10.1007/s13171-023-00317-7","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52730409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Weighted Least Squares Estimators for Chirp Like Model","authors":"D. Kundu, Swagata Nandi, Rhythm Grover","doi":"10.1007/s13171-023-00313-x","DOIUrl":"https://doi.org/10.1007/s13171-023-00313-x","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44204432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Farid Foroghi, S. Tahmasebi, M. Afshari, Francesco Buono
{"title":"Results on a Generalized Fractional Cumulative Entropy","authors":"Farid Foroghi, S. Tahmasebi, M. Afshari, Francesco Buono","doi":"10.1007/s13171-023-00316-8","DOIUrl":"https://doi.org/10.1007/s13171-023-00316-8","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41795360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Generalization of the Spatial Binary Model to the Longitudinal Spatial Setup","authors":"B. Sutradhar","doi":"10.1007/s13171-023-00319-5","DOIUrl":"https://doi.org/10.1007/s13171-023-00319-5","url":null,"abstract":"","PeriodicalId":46728,"journal":{"name":"Sankhya-Series A-Mathematical Statistics and Probability","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46088972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}