In this big data era, the roles of statisticians in academia and industries and of academic societies such as the Japan Statistical Society are gradually changing. The perspective of statistics seems to become much broader than ever. In this article, based on the author's own experience, activities of statisticians of past several decades are described, which are expected to be worth for rethinking the role that will be played by statisticians of present and coming ages.

The standardization has a function of eliminating such information as expectation and variance from its probability distribution. We shall characterize this function as a decomposition of the distributions into two mutually independent parts, one is expectation and variance, and the other is what this paper deals with. And we will define it, in more general sense than the standardization, as γ-decomposition. It is shown that the sp-curvature of saddlepoint gives the γ-decomposition. The sp-curvature successfully explains the asymptotic normality of distributions. A classical limit theorem, such as the de Moivre and Laplace's, can also be proved in terms of the γ-decomposition with sp-curvature.

Under the assumptions of continuous distribution and homogeneous variance, we consider multiple comparisons tests for the differences among mean responses in k samples. Hayter (1990) proposed single-step procedure as all-pairwise comparison test between ordered treatments in k samples under assuming normality. We propose closed testing procedures based on Bartholomew's tests. The proposed procedures are superior to Hayter (1990). Furthermore nonparametric closed testing procedures are discussed based on ranks. The closed testing procedures proposed in this paper are applicable for the models with unequal sample sizes.

Stress testing became more important on financial risk management after financial crisis of 2007–2009. The risk quantity is estimated based on the scenario that low frequency and large loss events occur on stress testing. The correlation among the variables is important, particularly the tail correlation is crucial on stress testing. In this paper, we propose the credit stress testing model with vine copula to consider detail of the tail correlation and compare this model with the expansion of one factor Merton model, which is used to evaluate the risk amount of credit portfolio. As a result, we find the average credit rating by this model clearly changes depending on the stress scenario, unlike one factor Merton model. We confirm this model captures the difference among the characteristics of industry sectors and provides the result depending on the industry sector of each borrower.

We investigate how a copula between risk factors takes portfolio diversification effect on market risk in both stressed and normal situations when the portfolio is comprised of stock and bond securities. In Japanese market over the past ten years, the movement of stock price and interest rate had shown positive correlation; in this situation a financial industry-standard practice of risk aggregation (such as variance-covariance method) provides large diversification effect on portfolio market risk, compared with the simple sum of stock risk and bond risk. In the European debt crisis since 2009, however, stock price plunge and interest rate surge occur at the same time; in such a stressed situation the diversification effect is considered to be limited. Hence, we consider copulas representing the dependency between risk factors in a stressed situation within the industry-standard framework of time series models. Devising copulas to capture the stressed situations even in normal periods as well as examining data in stressed both periods and areas, we measure the impact of the copulas in a stressed situation on the diversification effect and carry several implications.

For financial institutions, risk aggregation to calculate total economic capital is one of the main issue on integrated risk management. On risk aggregation, modeling association among marginal risks is quite important since they are strongly related. However, due to its complexity and lack of reliable data, it often has much of difficulty and uncertainty. Value-at-risk(VaR) is the most popular risk measure, but Embrechts et al. (2015) suggested that VaR is not robust to such uncertainty of dependence. For these reasons, it is beneficial to capture the model risk quantitatively by measuring fluctuation of total economic capital due to the dependence uncertainty. Rearrangement Algorithm(RA), proposed by Embrechts et al. (2013) enables us to calculate approximate upper and lower bounds of the aggregated risk capital among any dependence structures. On applying RA, it is sometimes required to discretize conditional tail distribution of marginals finely enough. This places considerable computational complexity on a real application of RA to integrated risk models. In this paper, we first show an integrated risk model which reduces the computational load on applying RA. Then calculate the bounds of total economic capital using RA. Lastly, we give some examinations and warnings based on our numerical results.