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2019  Estimation of finite mixture models of skew-symmetric circular distributions  共著   
Metrika  , Springer  , 未定  , 未定  , 2019/09   

概要(Abstract) Analysis of circular data is challenging, since the usual statistical methods are unsuitable and it is necessary to use circular periodic probabilistic models. Because some actual circular datasets exhibit asymmetry and/or multimodality, finite mixtures of symmetric circular distributions to model and fit these data have been investigated. However, it is necessary to question the predominant assumption that each component in the finite mixture models is symmetric. In this study, we consider a finite mixture model of possibly skewed circular distributions and discuss the expectation-maximization (EM) algorithm for the maximum likelihood estimate. It is shown that the maximum likelihood estimator is strongly consistent under some suitable conditions in a finite mixture of skew-symmetric circular distributions. A modified M-step in the EM algorithm is proposed in order to estimate the unknown parameter vectors effectively. To investigate the effectiveness of our proposed model with its estimation procedure, we provide a numerical example as well as data analysis using the records of the time of day of fatal traffic accidents. 


2019  Identifiability of asymmetric circular and cylindrical distributions  共著   
ArXiv  , Cornell University  , pp.1-14  , 2019/08   

概要(Abstract) A new method to prove the identifiability of asymmetric circular and cylindrical distributions, which utilizes Teicher's approach, is proposed. We use the simultaneous Diophantine approximations and the trigonometric moments of circular random variables to check some conditions of the proposed method. We prove the identifiability of a general sine-skewed circular distribution including the sine-skewed von Mises and sine-skewed wrapped Cauchy distributions, and a cylindrical distribution combining the sine-skewed von Mises distribution on the circle and the Weibull distribution on the non-negative linear under suitable parameter spaces. 


2019  A cylindrical distribution with heavy-tailed linear part  共著   
Japanese Journal of Statistics and Data Science  , Springer  , pp. 129-154  , 2019/06   

概要(Abstract) A cylindrical distribution whose linear part models heavy-tailedness is proposed. The conditional distribution of the linear variable given the circular variable is a generalized Pareto-type distribution. Therefore, it may not have any conditional moments; however, the mode and median have closed form expressions. The circular marginal distribution is a wrapped Cauchy distribution, and the conditional distribution of the circular variable given the
linear variable belongs to a family of symmetric distributions. These properties allow its application to cylindrical data whose linear observations may take large values, and whose circular observations are symmetric. As illustrative examples, the proposed distribution is fitted to two datasets, and the
results are compared with those by other cylindrical distributions that cannot model heavy-tailedness for the linear parts. 


2019  正弦関数に基づく非対称な円周分布の推定理論における諸問題について  共著   
数理解析研究所 講究録  , 京都大学  , 未定  , 未定  , 2019/05   

概要(Abstract) 正弦関数を用いた非対称な円周分布における, 三角モーメント, パラメーターの識別可能性およびフィッシャー情報行列の正値定符号性に関して,これまで明らかになっている研究結果の紹介を行った.  


2019  Multivariate skew distributions with mode-invariance through transformation of scale  共著   
Japanese Journal of Statistics and Data Science  , Springer  , pp. 1-17  , 2019/05   

概要(Abstract) The skew-symmetric distribution is often-used as a skew distribution, but it is not always unimodal even when the underlying distribution is unimodal. Recently, another type of skew distribution was proposed using the transformation of scale (ToS). It is always unimodal and shows the monotonicity of skewness. In this paper, a multivariate skew distribution is considered using the ToS. The skewness for the multivariate skew distribution is proposed and the monotonicity of skewness is shown. The proposed multivariate skew distribution is more flexible than the conventional multivariate skew-symmetric distributions. This is illustrated in numerical examples. Additional properties are also presented, including random number generation, half distribution, parameter orthogonality, non-degenerated Fisher information, entropy maximization distribution.  


2018  非対称な円周分布による有限混合分布とその推定について  共著   
数理解析研究所 講究録  , 京都大学  , 2091  , 96-115  , 2018/12   

概要(Abstract) 円周上の非対称な確率分布,およびそれらの有限混合モデルについて紹介する. 特に非対称な確率分布の有限混合モデルにおける最尤推定量を求めるためのアルゴリズムおよび推定量の一致性に関する結果を紹介する.  


2017  A tractable, parsimonious and flexible model for cylindrical data, with applications  共著   
Econometrics and Statistics  , Elsevier  , Volume 4  , 91-104  , 2017/10   

概要(Abstract) Weibull分布とsine-skewed von Mises分布(Abe & Pewsey, 2011)を組み合わせることにより、新しいシリンダー上の分布族を提案している。提案分布族の特徴として、正規化定数が単純であるにもかかわらず、既存のいくつかの分布を含むことや、周辺分布や条件付き分布が知られている既存の分布であるので乱数生成が容易であることが挙げられる。
Johnson & Wehrly (1978)は彼らの論文の中の最初の二つの分布に対して、``A major limitation of the two previous densities is that if $X$ and $\Theta$ are independent, then $\Theta$ is forced to be uniformly distributed on the circle''と述べているが、WeiSSVMはsine skewed circular分布の構造から, このような欠点に悩まされることはない。本論文では、さらに、WeiSSVM分布以外にも、Weibull分布を一般化Gamma分布で置き換えることにより、別の拡張の方法があることを指摘している。
後の比較のために、既存のシリンダー上の分布も紹介し、パラメータ推定の例として、blue periwinkleの移動方向と移動距離の組からなるデータに対して、最尤法を用いてパラメータ推定、AICとBICによるモデルの比較を行い、既存のモデルよりも優れていることを示した。
本論文で提案しているWeiSSVMモデルは集中パラメータκが線形部分と角度部分の独立性をコントロールしているので欠点と捉えられる可能性があるが、パラメータの節約になっていることから、利点としても捉えることができる。また、このモデルはその性質の良さから、幅広い範囲での応用が期待できる。実際、近年ではこのモデルを使用する研究者らはWeiSSVMモデルをAbe-Leyモデルと呼んでおり、応用的な研究で使い始めている(例えば、Lagona et al., 2015等)。

In this paper, we propose cylindrical distributions obtained by combining the sine-skewed von Mises distribution (circular part) with the Weibull distribution (linear part). This new model, the {WeiSSVM}, enjoys numerous advantages: simple normalizing constant and hence very tractable density, parameter-parsimony and interpretability, good circular-linear dependence structure, easy random number generation thanks to known marginal/conditional distributions, flexibility illustrated via excellent fitting abilities, and a straightforward extension to the case of directional-linear data. Inferential issues, such as independence testing, can easily be tackled with our model, which we apply on two real data sets. We conclude the paper by discussing future applications of our model. 


2017  Circular autocorrelation of stationary circular Markov processes  共著   
Statistical Inference for Stochastic Processes  , Springer  , Volume 20/ Issue 3  , pp. 275-290  , 2017/10   

概要(Abstract) The stationary Markov process is considered and its circular autocorrelation function is investigated. More specifically, the transition density of the stationary Markov circular process is defined by two circular distributions, and we elucidate the structure of the circular autocorrelation when one of these distributions is uniform and the other is arbitrary. The asymptotic properties of the natural estimator of the circular autocorrelation function are derived. Furthermore, we consider the bivariate process of trigonometric functions and provide the explicit form of its spectral density matrix. The validity of the model was assessed by applying it to a series of wind direction data. 


2016  Crown asymmetry in high latitude forests: disentangling the directional effects of tree competition and solar radiation  共著   
Oikos  , Wiley  , Volume 125 / Issue 7  , 1035-1043  , 2016/07   

概要(Abstract) 樹木は太陽光により光合成を行い、樹冠を拡大し、樹木同士で太陽光を巡った競争が発生する。また、高緯度の北方林では、太陽光の入射角度が低いことから、樹冠が非対称になる。これらの樹木間の競合(線形部分)と太陽光 (角度部分) の影響を明らかにするために、シリンダーモデルを用いてこれら2つの影響の度合いを定量化した。これにより、高緯度の森林においては、太陽の影響よりも、競合する樹木の影響が強いことが分かった。
Light foraging by trees is a fundamental process shaping forest communities. In heterogeneous light environments this behavior is expressed as plasticity of tree growth and the development of structural asymmetries. We studied the relative influence of neighborhood structure and directional solar radiation on horizontal asymmetry of tree crowns in late-successional high latitude (67–68°N) forests in northern Fennoscandia. We described crown asymmetries as crown vectors (i.e. horizontal vectors from stem center to crown center), which we obtained from canopy maps based on crown perimeter measurements in the field. To disentangle the influence of the two main determinants, inter-tree competition and directionality of above-canopy solar radiation at high latitudes, we applied circular statistical models, utilizing cylindrical distributions, to these data consisting of orientations and intensities of crown asymmetry. At the individual tree level, our model predicted crown asymmetry vectors from the current stand structure, and the predictions became better when the intensity of asymmetry (i.e. crown vector length) was higher. Competition was the main determinant of crown asymmetry for 2/3 of trees, and the model predictions improved when we incorporated the directionality of solar radiation. At the stand-level, these asymmetries had resulted in a small increment of the projected canopy area and an increased regularity of spatial structure. Our circular statistical modelling approach provided a quantitative evaluation of the relative importance of directionality of solar radiation and neighborhood stand structure, showing how both of these factors play a role in formation of crown asymmetries in high latitude forests. This approach further demonstrated the applicability of circular statistical modeling in ecological studies where the response variable has both orientation and intensity. 


2015  Discussion: "On families of distributions with shape parameters''   単著   
International Statistical Review  , Wiley  , 83/2  , 193-197  , 2015/08   

概要(Abstract) この論文は、Prof. JonesのDiscussion paperのdiscussantとして、招待されたDiscussion paperである。本論文では、変換後の非対称分布のモードが変換前の非対称分布と変わらない、モード不変性を持つような実数から実数への変換を紹介した。また、Jones and Pewsey (2012, Biometrics)の論文で``モーメント計算が困難である” と述べていたInverse Batschelet分布のモーメントの解析的表現を与えた。さらに、このような性質を持つような分布で他にも解析的表現が可能となる円周分布の例を与えた。 


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