Program

February 17, 2026 (Tuesday)

• 13:00–13:10
  Opening Remarks
  Yuichi Goto (Kyushu University)
• 13:10–13:40
  Speaker: Soma Nikai (Kyushu University)
  Title: Robust M-estimation of scatter matrices via precision structure shrinkage
  Abstract

  Tyler’s M-Estimator (TME) is a well-known method for robust covariance structure estimation, based on the idea of iteratively reweighting data points according to their Mahalanobis distances. Due to its simplicity, robustness, and efficiency, TME is widely used in fields such as robust statistics, anomaly detection, and signal processing – particularly in situations where data potentially contain outliers. While TME appears to offer high robustness, it is known that TME is vulnerable to a specific type of outliers known as clustered outliers, where outliers are concentrated within a narrow area. In this talk, we first report numerical experiments that suggest the source of the vulnerability lies in the process of estimating the inverse of covariance structure, i.e., the precision structure, within the TME algorithm. To address this issue, we propose an algorithm that targets the estimation of the precision structure. The proposed method explicitly incorporates the Efron–Morris (1976) approach for precision structure estimation of the TME algorithm. We demonstrate through numerical experiments that the proposed method exhibits high robustness not only against clustered outliers, but also against outliers that are due to heavy-tailed population distributions such as the t-distribution with small degrees of freedom. We evaluate the robustness of the proposed method in terms of the breakdown point and provide interpretations from various perspectives.

• 13:50–14:40
  Speaker: Gaspard Bernard (Academia Sinica)
  Title: Testing for sphericity under elliptical directions and potential temporal dependence
  Abstract

  It is well known that in a classical elliptical model, testing the rotational symmetry of the underlying distribution is equivalent to testing that a dispersion parameter is a multiple of the identity matrix. We consider the more general model of random vectors with elliptical directions and introduce some scenarios in which testing for rotational symmetry—or at least isotropy—is still equivalent to testing that the dispersion parameter is a multiple of the identity. In particular, since the elliptical direction model allows to depart from the i.i.d. assumption, our approach allows to consider scenarios in which temporal dependence of a certain type is present in the data generating process. We argue that, under these new assumptions, the classical spatial sign test is a very natural test statistic and show that, under certain mild conditions, it is asymptotically valid and has the same local asymptotic power as in the classical elliptical scenario. We then show that the spatial sign test is not only robust but also enjoys certain local asymptotic optimality properties when testing for sphericity when the underlying distribution is strongly heavy-tailed.

• 15:00–15:50
  Speaker: Marc Hallin (Université Libre de Bruxelles and Czech Academy of Science)
  Title: Multiple-attribute Lorenz functions and Gini indices: A measure-transportation approach
  Abstract

  Based on measure-transportation ideas and related concepts of quantile functions and regions, multiple-output extensions of the traditional single-attribute concepts of Lorenz and concentration functions and related Gini and Kakwani indices are proposed. These new concepts have a natural interpretation, either in terms of contributions of quantile regions to the expectation of some variable of interest, or in terms of the physical notions of work and energy, which sheds new light on the nature of economic and social inequalities. When based on center-outward quantile regions, the proposed concepts pave the way to a statistically sound definition, based on multiple variables, of the notion, so far limited to univariate characterizations, of middle-class, a notion of practical importance in various socio-economic and political contexts.

• 16:10–17:00
  Speaker: Masanobu Taniguchi (Waseda University)
  Title: Second order generalization of Hajek’s convolution theorem and its applications
  Abstract

  For a class of regular estimators, Hajek showed that the contiguous asymptotic distribution of regular estimator converges to a convolution of distribution of efficient estimator and the residual distribution, called as the Hajek convolution theorem. This provides the foundation of asymptotic efficiency etc of regular estimators. In this talk, introducing a class of second-order regular estimators by the valid Edgeworth expansion, we derive its second-order contiguous distribution, which is a convolution of the second-order efficient distribution and its second-order residual distribution, which is a second-oder generalization of Hajek’s convolution theorem. Then, we discuss the second-order efficiency etc. Also we introduce a second-order robustness for the second-order regular estimators. For a class of general minimum contrast estimators in time series models, the second-order robustness will be evaluated. Cowork with J.Hirukawa & M.Hallin.