{"title":"Model fitting using partially ranked data","authors":"M. Alvo, XiuWen Duan","doi":"10.1080/10485252.2023.2176180","DOIUrl":"https://doi.org/10.1080/10485252.2023.2176180","url":null,"abstract":"The importance of models for complete ranking data is well-established in the literature. Partial rankings, on the other hand, arise naturally when the set of objects to be ranked is relatively large. Partial rankings give rise to classes of compatible order preserving complete rankings. In this article, we define an exponential model for complete rankings and calibrate it on the basis of a random sample of partial rankings data. We appeal to the EM algorithm. The approach is illustrated in some simulations and in real data.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"5 1","pages":"587 - 600"},"PeriodicalIF":1.2,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80275203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cramér-von-Mises tests for the distribution of the excess over a confidence level","authors":"D. Gaigall, Julian Gerstenberg","doi":"10.1080/10485252.2023.2173958","DOIUrl":"https://doi.org/10.1080/10485252.2023.2173958","url":null,"abstract":"The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"246 1","pages":"529 - 561"},"PeriodicalIF":1.2,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76184514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic behaviour of the portmanteau tests in an integer-valued AR model","authors":"Jing Zhang, B. Li, Xiaohui Liu, Xinyue Wan","doi":"10.1080/10485252.2023.2175594","DOIUrl":"https://doi.org/10.1080/10485252.2023.2175594","url":null,"abstract":"The portmanteau test has been popular for diagnostic checking in time series models. Asymptotic properties of portmanteau tests have been exhaustively studied for real-valued time series model though, similar results for integer-valued autoregressive (INAR) models are not well documented, nevertheless. In view of this, we investigate the asymptotic behaviour of the Box-Pierce and Ljung-Box portmanteau tests in an INAR model. It turns out that these tests are chi-squared distributed asymptotically under mild conditions regardless of the process being stable or nearly unstable.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"30 1","pages":"562 - 586"},"PeriodicalIF":1.2,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74280802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Choosing shape parameters for regression in reproducing kernel Hilbert space and variable selection","authors":"Xin Tan, Yingcun Xia, Efang Kong","doi":"10.1080/10485252.2023.2164890","DOIUrl":"https://doi.org/10.1080/10485252.2023.2164890","url":null,"abstract":"The Gaussian radial basis function (RBF) is a widely used kernel function in kernel-based methods. The parameter in RBF, referred to as the shape parameter, plays an essential role in model fitting. In this paper, we propose a method to select the shape parameters for the general Gaussian RBF kernel. It can simultaneously serve for variable selection and regression function estimation. For the former, asymptotic consistency is established; for the latter, the estimation is as efficient as if the true or optimal shape parameters are known. Simulations and real examples are used to illustrate the method's performance of prediction by comparing it with other popular methods.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"70 1","pages":"514 - 528"},"PeriodicalIF":1.2,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86491419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric inference for interval data using kernel methods","authors":"Hoyoung Park, J. Loh, Woncheol Jang","doi":"10.1080/10485252.2022.2160980","DOIUrl":"https://doi.org/10.1080/10485252.2022.2160980","url":null,"abstract":"ABSTRACT Symbolic data have become increasingly popular in the era of big data. In this paper, we consider density estimation and regression for interval-valued data, a special type of symbolic data, common in astronomy and official statistics. We propose kernel estimators with adaptive bandwidths to account for variability of each interval. Specifically, we derive cross-validation bandwidth selectors for density estimation and extend the Nadaraya–Watson estimator for regression with interval data. We assess the performance of the proposed methods in comparison with existing kernel methods by extensive simulation studies and real data analysis.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"21 1","pages":"455 - 473"},"PeriodicalIF":1.2,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81559954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Testing axial symmetry by means of integrated rank scores","authors":"Š. Hudecová, M. Siman","doi":"10.1080/10485252.2022.2159399","DOIUrl":"https://doi.org/10.1080/10485252.2022.2159399","url":null,"abstract":"The article addresses the recently emerging inferential problem of testing axial symmetry up to a shift, which is useful even for testing certain hypotheses of exchangeability, independence, goodness-of-fit or equality of scale. In particular, it introduces a new test of axial symmetry based on integrated rank scores for directional quantile regression. The test outperforms existing competitors in terms of size, power, robustness, moment conditions or computational feasibility. All that is illustrated with a series of simulated examples.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"20 1","pages":"474 - 490"},"PeriodicalIF":1.2,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83047446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximum approximate Bernstein likelihood estimation in a two-sample semiparametric model","authors":"Zhong Guan","doi":"10.1080/10485252.2022.2158332","DOIUrl":"https://doi.org/10.1080/10485252.2022.2158332","url":null,"abstract":"Maximum likelihood estimators are proposed for the parameters and the underlying densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used to obtain the maximum approximate Bernstein likelihood estimates. The proposed method is illustrated by two real data from medical research and is shown by simulation to have better performance than the existing ones. Some asymptotic results are also presented and proved.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"7 1","pages":"437 - 453"},"PeriodicalIF":1.2,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87156439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimating POT second-order parameter for bias correction","authors":"Nan Zou","doi":"10.1080/10485252.2023.2226237","DOIUrl":"https://doi.org/10.1080/10485252.2023.2226237","url":null,"abstract":"The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the Peaks-Over-Threshold (POT) second-order parameter. For this second-order parameter, this paper introduces a penalized estimator that discourages it from being too close to zero. This paper then establishes this estimator's asymptotic consistency, uses it to correct the bias in the estimation of the stable tail dependence function, and illustrates its desirable empirical properties in the estimation of the extremal dependence structures.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"258 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77138146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric inference about increasing odds rate distributions","authors":"T. Lando, Idir Arab, P. E. Oliveira","doi":"10.1080/10485252.2023.2220050","DOIUrl":"https://doi.org/10.1080/10485252.2023.2220050","url":null,"abstract":"To improve nonparametric estimates of lifetime distributions, we propose using the increasing odds rate (IOR) model as an alternative to other popular, but more restrictive, ``adverse ageing'' models, such as the increasing hazard rate one. This extends the scope of applicability of some methods for statistical inference under order restrictions, since the IOR model is compatible with heavy-tailed and bathtub distributions. We study a strongly uniformly consistent estimator of the cumulative distribution function of interest under the IOR constraint. Numerical evidence shows that this estimator often outperforms the classic empirical distribution function when the underlying model does belong to the IOR family. We also study two different tests, aimed at detecting deviations from the IOR property, and we establish their consistency. The performance of these tests is also evaluated through simulations.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"8 4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78387434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extended Glivenko–Cantelli theorem and L 1 strong consistency of innovation density estimator for time-varying semiparametric ARCH model","authors":"Chen Zhong","doi":"10.1080/10485252.2022.2152813","DOIUrl":"https://doi.org/10.1080/10485252.2022.2152813","url":null,"abstract":"ABSTRACT This paper extends the classical Glivenko–Cantelli theorem for the empirical cumulative distribution function based on the innovations in the ARCH model with a slowly time-varying trend. In this semiparametric time-varying model, strong consistency for the innovation density estimator via kernel smoothing method is established, given that the trend and ARCH parameter estimators meet some mild conditions. Besides, the strong consistency for the Gaussian quasi maximum likelihood estimator (QMLE) in the time-varying ARCH parameter is established as well. Moreover, in terms of the existence of the trend in the data, two major nonparametric trend estimators, B-spline and kernel estimators, are shown to be appropriate for the strong consistency results.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"99 1","pages":"373 - 396"},"PeriodicalIF":1.2,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83605981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}