■ Books and Articles
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Article |
EM estimation of the B-spline copula with penalized pseudo-likelihood functions Statistical Papers 66(30) (Collaboration) 2025/01 |
| Language | English | | Publication Date | 2025/01 | | Type | Research Paper | | Peer Review | With peer review | | Title | EM estimation of the B-spline copula with penalized pseudo-likelihood functions | | Contribution Type | Joint Work | | Journal | Statistical Papers | | Journal Type | Another Country | | Publisher | Springer Nature | | Volume, Issue, Pages | 66(30) | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards | | Details | The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. We develop a modified EM algorithm, to maximize the penalized pseudo-likelihood function, wherein we use the smoothly clipped absolute deviation (SCAD) penalty function for the penalization term. We conduct simulation studies to demonstrate the stability of the proposed numerical procedure, show that penalization yields estimates with smaller mean-square errors when the true parameter matrix is sparse, and provide methods for determining tuning parameters and for model selection. We analyze as an example a data set consisting of birth and death rates from 237 countries, available at the website, “Our World in Data,” and we estimate the marginal density and distribution functions of those rates together with all parameters of our B-spline copula model. | |
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Bell numbers in Matsunaga's and Arima's Genjiko combinatorics: Modern perspectives and local limit theorems The Electronic Journal of Combinatorics 29(2) (Collaboration) 2022/04 |
| Language | English | | Publication Date | 2022/04 | | Type | Research Paper | | Peer Review | With peer review | | Title | Bell numbers in Matsunaga's and Arima's Genjiko combinatorics: Modern perspectives and local limit theorems | | Contribution Type | Joint Work | | Journal | The Electronic Journal of Combinatorics | | Journal Type | Another Country | | Volume, Issue, Pages | 29(2) | | Authorship | Lead author | | International coauthorship | International coauthorship | | Author and coauthor | Xiaoling Dou, Hsien-Kuei Hwang, Chong-Yi Li | | Details | We examine and clarify in detail the contributions of Yoshisuke Matsunaga (1694?–1744) to the computation of Bell numbers in the eighteenth century (in the Edo period), providing modern perspectives to some unknown materials that are by far the earliest in the history of Bell numbers. Later clarification and developments by Yoriyuki Arima (1714–1783), and several new results such as the asymptotic distributions (notably the corresponding local limit theorems) of a few closely related sequences are also given. | |
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Causality for CHARN models Scientiae Mathematicae Japaonicae 85,pp.59-74 (Single) 2021/06 |
| Language | English | | Publication Date | 2021/06 | | Type | Research Paper | | Peer Review | With peer review | | Title | Causality for CHARN models | | Contribution Type | Single Work | | Journal | Scientiae Mathematicae Japaonicae | | Journal Type | Another Country | | Volume, Issue, Pages | 85,pp.59-74 | | Total page number | 16 | | Authorship | Lead author,Last author,Corresponding author | | Author and coauthor | Xiaoling Dou | |
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Article |
Dependence properties of B-spline copulas Sankhya A 83,pp.283-311 (Collaboration) 2021/02 |
| Language | English | | Publication Date | 2021/02 | | Type | Research Paper | | Peer Review | With peer review | | Title | Dependence properties of B-spline copulas | | Contribution Type | Joint Work | | Journal | Sankhya A | | Journal Type | Another Country | | Volume, Issue, Pages | 83,pp.283-311 | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards | | Details | We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker’s distributions. The range of correlation of the B-spline copulas is examined, and the Fréchet–Hoeffding upper bound is proved to be attained when the number of B-spline functions goes to infinity. As the B-spline functions are well-known to be an order-complete weak Tchebycheff system from which the property of total positivity of any order follows for the maximum correlation case, the results given here extend classical results for the Bernstein copulas. In addition, we derive in terms of the Stirling numbers of the second kind an explicit formula for the moments of the related B-spline functions on the right half-line. | |
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The bivariate lack-of-memory distributions Sankhya A 81,pp.273-297 (Collaboration) 2019/12 |
| Language | English | | Publication Date | 2019/12 | | Type | Research Paper | | Peer Review | With peer review | | Title | The bivariate lack-of-memory distributions | | Contribution Type | Joint Work | | Journal | Sankhya A | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 81,pp.273-297 | | International coauthorship | International coauthorship | | Author and coauthor | Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki | | Details | We treat all the bivariate lack-of-memory (BLM) distributions in a unified approach and develop some new general properties of the BLM distributions, including joint moment generating function, product moments, and dependence structure. Necessary and sufficient conditions for the survival functions of BLM distributions to be totally positive of order two are given. Some previous results about specific BLM distributions are improved. In particular, we show that both the Marshall–Olkin survival copula and survival function are totally positive of all orders, regardless of parameters. Besides, we point out that Slepian’s inequality also holds true for BLM distributions. | |
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Article |
An investigation of a generalized least squares estimator for non-linear time series model Scientiae Mathematicae Japonicae 82,pp.29-44 (Single) 2019/07 |
| Language | English | | Publication Date | 2019/07 | | Type | Research Paper | | Peer Review | With peer review | | Title | An investigation of a generalized least squares estimator for non-linear time series model | | Contribution Type | Single Work | | Journal | Scientiae Mathematicae Japonicae | | Journal Type | Another Country | | Volume, Issue, Pages | 82,pp.29-44 | | Authorship | Lead author,Last author,Corresponding author | | Author and coauthor | Xiaoling Dou | | Details | Ochi(1983) proposed an estimator for the autoregressive coefficient of the first-order autoregressive model (AR(1)) by using two constants for the end points of the process. Classical estimators for AR(1), such as the least squares estimator, Burg's estimator, and Yule- Walker estimator are obtained as special cases by choice of the constants in Ochi's estimator. By writing the first-order autoregressive conditional heteroskedastic model, ARCH(1), in a form similar to that of AR(1), we extend Ochi's estimator to ARCH(1) models. This allows introducing analogues of the least squares estimator, Burg's estimator and Yule- Walker estimator, and we compare the relations of these with Ochi's estimator for ARCH(1) models. We then provide a simulation for AR(1) models and examine the performance of Ochi's estimator. Also, we simulate Ochi's estimator for ARCH(1) with different parameter values and sample sizes. | |
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Article |
Functional clustering of mouse ultrasonic vocalization data PLOS ONE 13(5),pp.e0196834 (Collaboration) 2018/05 |
| Language | English | | Publication Date | 2018/05 | | Type | Research Paper | | Peer Review | With peer review | | Title | Functional clustering of mouse ultrasonic vocalization data | | Contribution Type | Joint Work | | Journal | PLOS ONE | | Journal Type | Another Country | | Volume, Issue, Pages | 13(5),pp.e0196834 | | Authorship | Lead author,Corresponding author | | Author and coauthor | Xiaoling Dou, Shingo Shirahata, Hiroki Sugimoto | | Details | Mouse ultrasonic vocalizations (USVs) are studied in many fields of science. However, various noise and varied USV patterns in observed signals make complete automatic analysis difficult. We improve several methods to reduce noise, detect USV calls and automatically cluster USV calls. After reduction of noise and detection of USV calls, we consider USV calls as functional data and characterize them as USV functions with B-spline basis functions. For discontinuous USV calls, breakpoints in the USV functions are defined using multiple knots in the construction of the B-spline basis functions, and a hierarchical method is used to cluster the USV functions by shape. We finally show the performance of the proposed methods with USV data recorded for laboratory mice. | |
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Article |
Testing for Granger causality by use of Box-Cox transformations ASTE Special Issue on the “Financial & Pension Mathematical Science” pp.3-17 (Collaboration) 2016/03 |
| Language | Japanese | | Publication Date | 2016/03 | | Type | Research Paper | | Peer Review | With peer review | | Title | Testing for Granger causality by use of Box-Cox transformations | | Contribution Type | Joint Work | | Journal | ASTE Special Issue on the “Financial & Pension Mathematical Science” | | Journal Type | Japan | | Volume, Issue, Pages | pp.3-17 | | Authorship | Lead author,Corresponding author | | Author and coauthor | Ryunosuke Koike, Xiaoling Dou, Masanobu Taniguchi, Yujie Xue | |
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9. |
Article |
EM algorithms for estimating the Bernstein copula Computational Statistics & Data Analysis 93,pp.228-245 (Collaboration) 2016/01 |
| Language | English | | Publication Date | 2016/01 | | Type | Research Paper | | Peer Review | With peer review | | Title | EM algorithms for estimating the Bernstein copula | | Contribution Type | Joint Work | | Journal | Computational Statistics & Data Analysis | | Journal Type | Another Country | | Publisher | ELSEVIER | | Volume, Issue, Pages | 93,pp.228-245 | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, and Donald Richards | | Details | A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation–maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent various distributions flexibly and that the proposed EM algorithms work well for such data. | |
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Article |
Noise reduction and classification of mouse ultrasonic vocalization data ASTE Special Issue on the “Financial & Pension Mathematical Science” 12,pp.71-79 (Collaboration) 2015/03 |
| Language | English | | Publication Date | 2015/03 | | Type | Research Paper | | Peer Review | With peer review | | Title | Noise reduction and classification of mouse ultrasonic vocalization data | | Contribution Type | Joint Work | | Journal | ASTE Special Issue on the “Financial & Pension Mathematical Science” | | Journal Type | Japan | | Volume, Issue, Pages | 12,pp.71-79 | | Authorship | Lead author,Corresponding author | | Author and coauthor | Xiaoling Dou, Shingo Shirahata, Sugimoto Hiroki, Tsuyoshi Koide | |
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11. |
Article |
Recent developments on the construction of bivariate distributions with fixed marginals Journal of Statistical Distributions and Applications 1(14) (Collaboration) 2014/06 |
| Language | English | | Publication Date | 2014/06 | | Type | Research Paper | | Peer Review | With peer review | | Title | Recent developments on the construction of bivariate distributions with fixed marginals | | Contribution Type | Joint Work | | Journal | Journal of Statistical Distributions and Applications | | Journal Type | Another Country | | Publisher | Springer Nature | | Volume, Issue, Pages | 1(14) | | International coauthorship | International coauthorship | | Author and coauthor | Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki, Jin-Sheng Huang | | Details | Constructing a bivariate distribution with specific marginals and correlation has been a challenging problem since 1930s. In this survey we shall focus on the recent developments on the FGM-related distributions, including Sarmanov and Lee’s distributions, Baker’s distributions and Bayramoglu’s distributions. This complements the most recent works of (i) the review by Sarabia and Gómez-Déniz (2008, SORT) and (ii) the monograph by Balakrishnan and Lai (2009, Springer). Some new results are provided. | |
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12. |
Article |
Influence analysis in quantitative trait loci detection Biometrical Journal 56(4),pp.697-719 (Collaboration) 2014/04 |
| Language | English | | Publication Date | 2014/04 | | Type | Research Paper | | Peer Review | With peer review | | Title | Influence analysis in quantitative trait loci detection | | Contribution Type | Joint Work | | Journal | Biometrical Journal | | Journal Type | Another Country | | Volume, Issue, Pages | 56(4),pp.697-719 | | Authorship | Lead author,Corresponding author | | Author and coauthor | Xiaoling Dou, Satoshi Kuriki, Akiteru Maeno, Toyoyuki Takada, Toshihiko Shiroishi | | Details | This paper presents systematic methods for the detection of influential individuals that affect the log odds (LOD) score curve. We derive general formulas of influence functions for profile likelihoods and introduce them into two standard quantitative trait locus detection methods—the interval mapping method and single marker analysis. Besides influence analysis on specific LOD scores, we also develop influence analysis methods on the shape of the LOD score curves. A simulation-based method is proposed to assess the significance of the influence of the individuals. These methods are shown useful in the influence analysis of a real dataset of an experimental population from an F2 mouse cross. By receiver operating characteristic analysis, we confirm that the proposed methods show better performance than existing diagnostics. | | URL for researchmap | https://doi.org/10.1002/bimj.201200178 | |
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13. |
Article |
Dependence structures and asymptotic properties of Baker's distributions with fixed marginals Journal of Statistical Planning and Inference 143(8),pp.1343-1354 (Collaboration) 2013/03 |
| Language | English | | Publication Date | 2013/03 | | Type | Research Paper | | Peer Review | With peer review | | Title | Dependence structures and asymptotic properties of Baker's distributions with fixed marginals | | Contribution Type | Joint Work | | Journal | Journal of Statistical Planning and Inference | | Journal Type | Another Country | | Publisher | ELSEVIER | | Volume, Issue, Pages | 143(8),pp.1343-1354 | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin | | Details | We investigate the properties of Baker's (2008) bivariate distributions with fixed marginals and their multivariate extensions. The properties include the weak convergence to the Fréchet–Hoeffding upper bound, the product-moment convergence, as well as the dependence structures TP2 (totally positive of order 2), or MTP2 (multivariate TP2). In proving the weak convergence, a generalized local limit theorem for binomial distribution is provided. | |
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14. |
Article |
Dependence structure of bivariate order statistics with applications to Bayramouglu's distributions Journal of Multivariate Analysis 114,pp.201-208 (Collaboration) 2013/02 |
| Language | English | | Publication Date | 2013/02 | | Type | Research Paper | | Peer Review | With peer review | | Title | Dependence structure of bivariate order statistics with applications to Bayramouglu's distributions | | Contribution Type | Joint Work | | Journal | Journal of Multivariate Analysis | | Journal Type | Another Country | | Publisher | ELSEVIER | | Volume, Issue, Pages | 114,pp.201-208 | | International coauthorship | International coauthorship | | Author and coauthor | J. S. Huang, Xiaoling Dou, Satoshi Kuriki, G. D. Lin | |
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15. |
Article |
Comparisons of B-spline procedures with kernel procedures in estimating regression functions and their derivatives Journal of the Japanese Society of Computational Statistics 22,pp.57-77 (Collaboration) 2009/01 |
| Language | English | | Publication Date | 2009/01 | | Type | Research Paper | | Peer Review | With peer review | | Title | Comparisons of B-spline procedures with kernel procedures in estimating regression functions and their derivatives | | Contribution Type | Joint Work | | Journal | Journal of the Japanese Society of Computational Statistics | | Journal Type | Japan | | Volume, Issue, Pages | 22,pp.57-77 | | Authorship | Lead author,Corresponding author | | Author and coauthor | Xiaoling Dou, Shingo Shirahata | | Details | There are several methods to estimate regression functions and their derivatives. Among them, B-spline procedures and kernel procedures are known to be useful. However, at present, it is not determined which procedure is better than the others. In this paper, we investigate the performance of the procedures by computer simulations. | |
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Article |
Discriminant analysis for functional data: linear methods and functional subspace methods Bulletin of the Computational Statistics of Japan pp.13-30 (Collaboration) 2007/07 |
| Language | Japanese | | Publication Date | 2007/07 | | Type | Research Paper | | Peer Review | With peer review | | Title | Discriminant analysis for functional data: linear methods and functional subspace methods | | Contribution Type | Joint Work | | Journal | Bulletin of the Computational Statistics of Japan | | Journal Type | Japan | | Volume, Issue, Pages | pp.13-30 | | Authorship | Lead author,Corresponding author | | Author and coauthor | Xiaoling Dou, Shingo Shirahata, Wataru Sakamoto | | Details | In discriminant analysis of functional data, several linear methods have been proposed, such as, filtering method, penalized discriminant analysis and functional linear discriminant analysis. However, if the size of training data is small or if it can not be assumed that the data in each class are from multivariate normal populations with equal covariance matrices, there is no guarantee that linear methods are always available.
To solve this problem, we propose nonlinear discriminant analysis methods called Functional Subspace Methods (FSMs) based on functional principal component expansion. FSMs include Functional Subspace Method and Functional CLAFIC Method. These procedures do not require any knowledge on the underlying distributions of populations, but linear discriminant analysis methods do. Furthermore, our methods can be carried out more rapidly than the traditional subspace methods, because they can be computed with lower dimensions. To show that the functional subspace methods are effective, we compare them with the filtering method. As a result, the functional subspace methods give good discrimination. Particularly, when the size of training data is small they can give more stable results than the filtering method. | |
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