Pub Date : 2019-04-01DOI: 10.3103/S1066530719020030
A. L’Moudden, É. Marchand
{"title":"On Predictive Density Estimation under α-Divergence Loss","authors":"A. L’Moudden, É. Marchand","doi":"10.3103/S1066530719020030","DOIUrl":"https://doi.org/10.3103/S1066530719020030","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"28 1","pages":"127 - 143"},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719020030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47698685","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}
Pub Date : 2019-02-09DOI: 10.3103/S1066530719020029
T. Kutta, N. Bissantz, J. Chown, H. Dette
{"title":"The Empirical Process of Residuals from an Inverse Regression","authors":"T. Kutta, N. Bissantz, J. Chown, H. Dette","doi":"10.3103/S1066530719020029","DOIUrl":"https://doi.org/10.3103/S1066530719020029","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"28 1","pages":"104 - 126"},"PeriodicalIF":0.5,"publicationDate":"2019-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719020029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44415720","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}
Pub Date : 2019-02-05DOI: 10.3103/s1066530718040014
B. Levit
For the Hardy classes of functions analytic in the strip around real axis of a size 2β, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design.In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case β → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.
{"title":"On Optimal Cardinal Interpolation","authors":"B. Levit","doi":"10.3103/s1066530718040014","DOIUrl":"https://doi.org/10.3103/s1066530718040014","url":null,"abstract":"For the Hardy classes of functions analytic in the strip around real axis of a size 2<i>β</i>, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design.In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case <i>β</i> → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"294 ","pages":"245-267"},"PeriodicalIF":0.5,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519673","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}
Pub Date : 2019-02-05DOI: 10.3103/s1066530718040038
M. V. Boldin, M. N. Petriev
We consider a stationary linear AR(p) model with observations subject to gross errors (outliers). The distribution of outliers is unknown and arbitrary, their intensity is γn−1/2 with an unknown γ, n is the sample size. The autoregression parameters are unknown, they are estimated by any estimator which is n1/2-consistent uniformly in γ ≤ Γ < ∞. Using the residuals from the estimated autoregression, we construct a kind of empirical distribution function (e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. We obtain a stochastic expansion of this e.d.f., which enables us to construct a test of Pearson’s chi-square type for testing hypotheses about the distribution of innovations. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting level with respect to γ in a neighborhood of γ = 0.
{"title":"On the Empirical Distribution Function of Residuals in Autoregression with Outliers and Pearson’s Chi-Square Type Tests","authors":"M. V. Boldin, M. N. Petriev","doi":"10.3103/s1066530718040038","DOIUrl":"https://doi.org/10.3103/s1066530718040038","url":null,"abstract":"We consider a stationary linear AR(<i>p</i>) model with observations subject to gross errors (outliers). The distribution of outliers is unknown and arbitrary, their intensity is <i>γn</i><sup>−1/2</sup> with an unknown <i>γ</i>, <i>n</i> is the sample size. The autoregression parameters are unknown, they are estimated by any estimator which is <i>n</i><sup>1/2</sup>-consistent uniformly in <i>γ</i> ≤ Γ < ∞. Using the residuals from the estimated autoregression, we construct a kind of empirical distribution function (e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. We obtain a stochastic expansion of this e.d.f., which enables us to construct a test of Pearson’s chi-square type for testing hypotheses about the distribution of innovations. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting level with respect to <i>γ</i> in a neighborhood of <i>γ</i> = 0.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"20 1","pages":"294-311"},"PeriodicalIF":0.5,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519657","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}
Pub Date : 2019-01-01DOI: 10.3103/S1066530719010010
Y. Hamura, T. Kubokawa
{"title":"Bayesian Predictive Distribution for a Negative Binomial Model","authors":"Y. Hamura, T. Kubokawa","doi":"10.3103/S1066530719010010","DOIUrl":"https://doi.org/10.3103/S1066530719010010","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"28 1","pages":"1 - 17"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719010010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69418784","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}
Pub Date : 2018-10-16DOI: 10.3103/S1066530719030025
R. Rimal, M. Pensky
{"title":"Density Deconvolution with Small Berkson Errors","authors":"R. Rimal, M. Pensky","doi":"10.3103/S1066530719030025","DOIUrl":"https://doi.org/10.3103/S1066530719030025","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"28 1","pages":"208 - 227"},"PeriodicalIF":0.5,"publicationDate":"2018-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719030025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42599170","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}
Pub Date : 2018-10-01DOI: 10.3103/S1066530718040026
E. Caron, S. Dede
{"title":"Asymptotic Distribution of Least Squares Estimators for Linear Models with Dependent Errors: Regular Designs","authors":"E. Caron, S. Dede","doi":"10.3103/S1066530718040026","DOIUrl":"https://doi.org/10.3103/S1066530718040026","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"27 1","pages":"268 - 293"},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530718040026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48254035","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}
Pub Date : 2018-10-01DOI: 10.3103/S106653071804004X
B. Berckmoes, G. Molenberghs
{"title":"On the Asymptotic Behavior of the Contaminated Sample Mean","authors":"B. Berckmoes, G. Molenberghs","doi":"10.3103/S106653071804004X","DOIUrl":"https://doi.org/10.3103/S106653071804004X","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"27 1","pages":"312 - 323"},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S106653071804004X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48404552","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}
Pub Date : 2018-07-23DOI: 10.3103/S106653071901006X
L. Klebanov, I. Volchenkova
{"title":"Outliers and the Ostensibly Heavy Tails","authors":"L. Klebanov, I. Volchenkova","doi":"10.3103/S106653071901006X","DOIUrl":"https://doi.org/10.3103/S106653071901006X","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"28 1","pages":"74 - 81"},"PeriodicalIF":0.5,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S106653071901006X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43378283","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}
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