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Mathematical Methods of Statistics最新文献

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Multi-level Bayes and MAP Monotonicity Testing 多层次贝叶斯和MAP单调性检验
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-09-20 DOI: 10.3103/S1066530720010032
Yu. Golubev, C. Pouet
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引用次数: 2
A Multiple Hypothesis Testing Approach to Detection Changes in Distribution 分布变化检测的多假设检验方法
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-08-05 DOI: 10.3103/s1066530719020054
G. Golubev, M. Safarian
{"title":"A Multiple Hypothesis Testing Approach to Detection Changes in Distribution","authors":"G. Golubev, M. Safarian","doi":"10.3103/s1066530719020054","DOIUrl":"https://doi.org/10.3103/s1066530719020054","url":null,"abstract":"Let <i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>,... be independent random variables observed sequentially and such that <i>X</i><sub>1</sub>,..., <i>X</i><sub><i>θ</i>−1</sub> have a common probability density <i>p</i><sub><i>0</i></sub>, while <i>X</i><sub><i>θ</i></sub>, <i>X</i><sub><i>θ</i>+1</sub>,... are all distributed according to <i>p</i><sub>1</sub> ≠ <i>p</i><sub>0</sub>. It is assumed that <i>p</i><sub>0</sub> and <i>p</i><sub>1</sub> are known, but the time change <i>θ</i> ∈ ℤ<sup>+</sup> is unknown and the goal is to construct a stopping time <i>τ</i> that detects the change-point <i>θ</i> as soon as possible. The standard approaches to this problem rely essentially on some prior information about <i>θ</i>. For instance, in the Bayes approach, it is assumed that <i>θ</i> is a random variable with a known probability distribution. In the methods related to hypothesis testing, this a priori information is hidden in the so-called average run length. The main goal in this paper is to construct stopping times that are free from a priori information about <i>θ.</i> More formally, we propose an approach to solving approximately the following minimization problem:<span>$$Delta(theta;{tau^alpha})rightarrowmin_{tau^alpha};;text{subject};text{to};;alpha(theta;{tau^alpha})leqalpha;text{for};text{any};thetageq1,$$</span>where <i>α</i>(<i>θ; τ</i>) = P<sub><i>θ</i></sub>{<i>τ &lt; θ</i>} is <i>the false alarm probability</i> and <i>Δ</i>(<i>θ</i>; <i>τ</i>) = E<sub><i>θ</i></sub>(<i>τ − θ</i>)<sub>+</sub> is <i>the average detection delay</i> computed for a given stopping time <i>τ</i>. In contrast to the standard CUSUM algorithm based on the sequential maximum likelihood test, our approach is related to a multiple hypothesis testing methods and permits, in particular, to construct universal stopping times with nearly Bayes detection delays.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519656","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}
引用次数: 1
An Asymptotically Optimal Transform of Pearson’s Correlation Statistic Pearson相关统计量的渐近最优变换
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-07-26 DOI: 10.3103/S1066530719040057
I. Pinelis
{"title":"An Asymptotically Optimal Transform of Pearson’s Correlation Statistic","authors":"I. Pinelis","doi":"10.3103/S1066530719040057","DOIUrl":"https://doi.org/10.3103/S1066530719040057","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719040057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47398748","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}
引用次数: 2
Central Limit Theorems for Conditional Empirical and Conditional U-Processes of Stationary Mixing Sequences 平稳混合序列的条件经验过程和条件U过程的中心极限定理
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-07-01 DOI: 10.3103/S1066530719030013
S. Bouzebda, B. Nemouchi
{"title":"Central Limit Theorems for Conditional Empirical and Conditional U-Processes of Stationary Mixing Sequences","authors":"S. Bouzebda, B. Nemouchi","doi":"10.3103/S1066530719030013","DOIUrl":"https://doi.org/10.3103/S1066530719030013","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719030013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43823131","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}
引用次数: 11
State Occupation Probabilities in Non-Markov Models 非马尔可夫模型中的状态占用概率
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-05-31 DOI: 10.3103/S1066530719040033
Morten Overgaard
{"title":"State Occupation Probabilities in Non-Markov Models","authors":"Morten Overgaard","doi":"10.3103/S1066530719040033","DOIUrl":"https://doi.org/10.3103/S1066530719040033","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719040033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42112674","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}
引用次数: 8
Density Estimation for RWRE RWRE的密度估计
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-05-03 DOI: 10.3103/s1066530719010022
A. Havet, M. Lerasle, É. Moulines
{"title":"Density Estimation for RWRE","authors":"A. Havet, M. Lerasle, É. Moulines","doi":"10.3103/s1066530719010022","DOIUrl":"https://doi.org/10.3103/s1066530719010022","url":null,"abstract":"We consider the problem of nonparametric density estimation of a random environment from the observation of a single trajectory of a random walk in this environment. We build several density estimators using the beta-moments of this distribution. Then we apply the Goldenschluger-Lepski method to select an estimator satisfying an oracle type inequality. We obtain non-asymptotic bounds for the supremum norm of these estimators that hold when the RWRE is recurrent or transient to the right. A simulation study supports our theoretical findings.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519642","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}
引用次数: 1
On the Power of Pearson’s Test under Local Alternatives in Autoregression with Outliers 有离群值的自回归中局部选择下Pearson检验的威力
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-05-03 DOI: 10.3103/s1066530719010046
M. V. Boldin
{"title":"On the Power of Pearson’s Test under Local Alternatives in Autoregression with Outliers","authors":"M. V. Boldin","doi":"10.3103/s1066530719010046","DOIUrl":"https://doi.org/10.3103/s1066530719010046","url":null,"abstract":"We consider a stationary linear <i>AR</i>(<i>p</i>) model with contamination (gross errors in the observations). The autoregression parameters are unknown, as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of the empirical distribution function is defined and a test of Pearson’s chi-square type is constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of this test under local alternatives and establish its qualitative robustness under the hypothesis and alternatives.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519654","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}
引用次数: 7
A Large Deviation Approximation for Multivariate Density Functions 多元密度函数的大偏差近似
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-05-03 DOI: 10.3103/s1066530719010058
C. Joutard
{"title":"A Large Deviation Approximation for Multivariate Density Functions","authors":"C. Joutard","doi":"10.3103/s1066530719010058","DOIUrl":"https://doi.org/10.3103/s1066530719010058","url":null,"abstract":"We establish a large deviation approximation for the density of an arbitrary sequence of random vectors, by assuming several assumptions on the normalized cumulant generating function and its derivatives. We give two statistical applications to illustrate the result, the first one dealing with a vector of independent sample variances and the second one with a Gaussian multiple linear regression model. Numerical comparisons are eventually provided for these two examples.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519655","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}
引用次数: 1
A Semi-Parametric Mode Regression with Censored Data 带截尾数据的半参数模式回归
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-05-03 DOI: 10.3103/s1066530719010034
S. Khardani
{"title":"A Semi-Parametric Mode Regression with Censored Data","authors":"S. Khardani","doi":"10.3103/s1066530719010034","DOIUrl":"https://doi.org/10.3103/s1066530719010034","url":null,"abstract":"In this work we suppose that the random vector (<i>X</i>, <i>Y</i>) satisfies the regression model <i>Y</i> = <i>m</i>(<i>X</i>) + <i>ϵ</i>, where <i>m</i>(·) belongs to some parametric class {<span>({m_beta}(cdot):beta in mathbb{K})</span>} and the error <i>ϵ</i> is independent of the covariate <i>X</i>. The response <i>Y</i> is subject to random right censoring. Using a nonlinear mode regression, a new estimation procedure for the true unknown parameter vector <i>β</i><sub>0</sub>is proposed that extends the classical least squares procedure for nonlinear regression. We also establish asymptotic properties for the proposed estimator under assumptions of the error density. We investigate the performance through a simulation study.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519674","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}
引用次数: 2
On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression 自回归中局部选择下拟合检验的渐近幂
IF 0.5
Mathematical Methods of Statistics Pub Date : 2019-04-01 DOI: 10.3103/S1066530719020042
M. Boldin
{"title":"On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression","authors":"M. Boldin","doi":"10.3103/S1066530719020042","DOIUrl":"https://doi.org/10.3103/S1066530719020042","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3103/S1066530719020042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69418834","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}
引用次数: 2
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