The theoretical development of statistical inference was started by R. A. Fisher in 1920s and contributed by A. Wald, L. LeCam, C. R. Rao, R. R. Bahadur, J. Kiefer, J. Wolfowitz and others in a systematic way in 1950s, and its theory was completed for the present. After that, based on the first order asymptotic theory that had been established until then and under consideration of a general resolution of Fisher's conjecture, the higher order asymptotics has been studied very hard by B. Efron, J. Pfanzagl, J. K. Ghosh, K. Takeuchi and the author among others. In this article, we will trace the history of ``deepening" and ``progress" in statistical inference around the development of higher order asymptotic theory.

When creating and releasing official microdata, both technical and legal methods are applied to protect the confidentiality of personal information contained in the data. Specifically, the creation and release of microdata requires a legal definition of personal information, the statutory interpretation of the relevant legal framework, advanced statistical systems and an ongoing optimization of statistical methods used in the creation of microdata. This paper identifies the methodological parameters for the creation and release of official microdata from the standpoint of statistical institutions and data users, and suggests suitable anonymization methods for official microdata in Japan.

Angular data arise in environmental science and meteorology as wind direction, in ecology as animal movement, and in molecular science as dihedral angle, etc. Also, the time of an event may be viewed as an angle on a 24 hour clock. Cardioid, von Mises and wrapped Cauchy distributions as symmetric distributions on the circle are well known in the literature. This article reviews recent developments, mainly after 2000, in the distribution theory for directional data which include angular observations. The topics include new symmetric distributions which contain cardioid, von Mises and wrapped Cauchy distributions as special cases, asymmetric distributions, distributions on the (hyper-) sphere, torus, cylinder and disc, together with their applications.

We review convergence rate analyses about multiple kernel leaning (MKL) by regularization methods and a Bayes method. As for regularization methods, we show convergence rates for ℓ₁ and elastic-net regularizations. The elastic-net regularization is a composition of an ℓ₁-regularizer for inducing the sparsity and an ℓ₂-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non-zero components of the ground truth is relatively small, and show sharper convergence rates than the learning rates ever shown for both ℓ₁ and elastic-net regularizations. Moreover, we show that, using a Bayesian method with Gaussian process priors, we don't need a strong conditions on the design to achieve a fast learning rate.