In this article, I overview the statistical analysis on human and social phenomena in super smart society by using large-scale data from the perspectives of business/marketing problems and discuss their statistical modeling for the future developments. Specifically, regarding statistical modeling in the business field in the modern society envisioned by Society 5.0, I first divide topics into three categories: (1) personalization, (2) high-dimensional sparsity, (3) networks and communities, and then I look back at our research and look ahead to these issues. Furthermore, by considering extensive advances in machine learning and AI technology, I discuss approaches to linking statistical modeling of human and social data to business decision-making.

Time series data often include missing values, and statistical modeling that deals with missing values is needed. Typically, a state-space model is used to impute missing values. However, this approach implicitly assumes that the missing mechanism is missing at random; thus, the estimator may be biased when the missing mechanism is not missing at random. In this study, we construct and incorporate the missing mechanism to reduce the bias of the estimator. The model parameter is estimated by the Monte Carlo Expectation-Maximization (MCEM) algorithm. Monte Carlo simulation is conducted to investigate the effectiveness of our proposed procedure.

This paper shows some models to analyze the structure of symmetry for contingency tables in my several works. It shows the models of symmetry, the decompositions for models of symmetry, and the measures for representing the degree of departure from symmetry.

This paper deals with two topics. One is higher-order local power comparison of tests related to Bartlett-type adjustments, and the other is nonparametric kernel type density estimation. It is well known that the chi-squared approximation for the log likelihood ratio (LR) statistic is improved via mean correction, i.e., division (equivalently, multiplication) of the LR statistic by a suitable constant. We begin with the Bartlett correctability of the LR statistic and introduce general methods of improving the chi-squared approximations for several famous statistics rather than the LR statistic. We then briefly discuss comparisons of tests under a sequence of local alternatives. On the other hand, we also review recent issues on asymmetric kernel density estimation for nonnegative data, which is a remedy of the boundary bias problem of the commonly used location-scale-type Rosenblatt–Parzen kernel method.

This article reviews recent developments in applying clustering methods to econometrics. Panel data are data with multiple observational units over multiple time points, which have the advantage of easily accounting for heterogeneity among observational units. Cluster analysis assumes that a few groups describe heterogeneity and is thus useful in both implementation and interpretation. However, to apply it to economic analysis, existing methods need to be extended to accommodate the characteristics of economic data and economic models. Structural breaks become issues when analyzing relatively long time series data, and this paper discusses estimation methods that accommodate structural changes. It also discusses how to incorporate cluster analysis into instrumental variables methods and the generalized method of moments used for models with endogeneity problems.