In the context of traditional risk theory for an insurance company, an important problem is ``dividend strategy", that is, how the portion where the insurance company's surplus exceeds a level of barrier will be paid to the shareholders as dividends. The optimal dividend barrier is defined as the level of the barrier that maximizes the expected discounted dividends until ruin. In this paper, based on the M-estimation method, we estimate the optimal dividend barrier from a sample path of the insurance company's surplus process. To show the consistency for the estimator, the uniformly convergence of the objective function is needed and this result is known as the Glivenko-Cantelli theorem. The Glivenko-Cantelli theorem describes the entropy measuring the magnitude of the functional family and how the family is easy to converge uniformly. We first show the boundedness of the uniform entropy for a family of objective functions and the uniform convergence. This result implies that the constructed M-estimator is consistent. To show the boundedness of the uniform entropy, it is shown that the family of objective functions belongs with VC-subgraph class. Finally, we confirm the uniform convergence of the objective function and the consistency of the optimal dividend barrier estimator through simulation.

This paper clarifies the influence of natural disasters on household income and relations with poverty in rural Vietnam. Vietnam is a country with many natural disasters like Japan. Therefore, the effects of natural disasters on the household welfare in rural areas where many poor people stay are concerning point for many researchers. Arouri et al. (2015) analysed this problem using household level microdata, VHLSS (Vietnam Household Living Standards). However, their analysis shows only the average impact that natural disasters have on household incomes and the influence on the income distribution is not captured. Therefore, we verified the effect on the income distribution using quantile regression method. As a result, it was found that drought has a relatively great influence on low-income groups. However, the estimated impact of natural disasters might be biased due to endogeneity. We analysed the effects of these natural disasters considering endogeneity bias although they are preliminary because panel data was not available.

Park and Tsuchiya (2017) conducted a mail survey to determine residents\rq{} consciousness in a particular Japanese city, Tachikawa city, Tokyo. Ascertaining the consciousness of residents of smaller administrative divisions would be even more useful to better plan suitable services for the residents. However, there are concerns that such subdividing could reduce the sample size of respondents within each division, and the conventional approach used in public administration research might yield unreasonable estimates of consciousness level. We thus conducted a hybrid type confidence interval and adopted a ``model-based approach" to analyze the survey data, and compared the results with results obtained using the conventional approach. We found that the model-based approach dramatically reduced several large differences observed between estimates in each neighborhood and the lengths of the confidence intervals, both originally provided by the conventional approach. We also assessed the model-based approach by a Monte Carlo simulation study and comparison with recent census results for small areas in Japan. Although the model-based approach is well known in the field of small-area estimation, this is, to the best of our knowledge, the first study in Japan to adopt this approach for an analysis of a consciousness survey at small-area (cho-chome) level.

In this paper, we introduce new developments of theories and methodologies in high-dimensional statistical analysis. Recently, Aoshima and Yata (2018a) have provided a noise model called the strongly spiked eigenvalue (SSE) model. Since the noise associated with high dimensional data is huge and non-sparse, the potential geometric structure of the data is destroyed and it is difficult to guarantee the accuracy for statistical inferences. In theory, the high-dimensional asymptotic normality that forms the basis of high-dimensional statistical analysis is not established under the SSE model. Aoshima and Yata (2018a) have developed a data transformation technique that avoids strongly spiked-noise spaces by precisely analyzing the huge noise structure. Using this method, the data is transformed into the non-strongly spiked eigenvalue (NSSE) model, which highlights the geometric structure of the latent space and enables highly accurate high-dimensional statistical inference. Aoshima and Yata (2018b) have applied this methodology to create a new theory for high-dimensional discriminant analysis. In this current paper, we explain the latest developments of high-dimensional statistical analysis while appropriately introducing literature.