Unlike the principles of traditional economics that substitution possibility holds for goods with monetary equivalency, mental accounting elaborates these goods would have different criteria values to consumers depending on purposes of its use and circumstances at purchase. Aided by modeling of inter-purchase duration that accommodates mental conditions changes captured by two latent variables, i.e. mental loading and household goods stock value, our research primarily intends to reveal how consumer's mental factor impacts consumer purchase behavior. Viewing from behavioral economics, the research attempts to comprehend consumer purchase behaviors that are seemingly irrational from traditional economics viewpoints. The model is derived from threshold-based modeling framework that incorporates consumer heterogeneity in a hierachical Bayesian manner, and modeling parameters are estimated using Markov Chain Monte Carlo (MCMC) mehod. Empirical studies have been exploited with ID-POS data of a retailer shop, and results indicate that our model outperforms by having consumer mental conditions changes into consideration at times of purchase.

This paper explores the effect of household real estate and financial asset ownership on household members' choice of employment. Analysis was conducted based on individual data from the Japanese National Survey of Family Income and Expenditure, which contains data on household members' employment, the composition of household incomes and the asset ownership of household members. Results suggest that the share of ``risky" assets including stocks and bonds among total household savings has a negative effect on head of households' employment, although the observed effect was limited. Results also show that real estate ownership has a negative effect on head of households' employment. These results indicate a theoretical possibility that the accumulation of household assets can motivate head of households to choose non-employment. The results also show a negative effect of residential land prices on head of households' employment.

In this paper, we introduce various multivariate stochastic volatility models and multivariate realized stochastic volatility models in the literature for the multiple asset returns, and discuss efficient Bayesian estimation methods using Markov chain Monte Carlo simulation.

Donald Rubin and Roderick Little have developed important basic theory of missing data analysis (e.g., Rubin (1976), Little and Rubin (1987, 2002)). They, however, have used useful but ambiguous notation Y_obs, Y_mis, so that it often causes misunderstanding. Using the precise notation, proper proofs are given for some statements on missing data analysis. Those include understanding comprehensively the method of maximum likelihood, giving a concise consistency proof of MLE, and clarifying relationship between MAR and conditional independence, role of the parameter distinction and efficacy of inclusion of auxiliary variables.

On estimating financial volatility models, Realized Stochastic Volatility (RSV) models use the information not only returns but also realized volatility measures, and it enables us to estimate the models efficiently.There are two popular approaches for estimating the RSV models; one is the Bayesian Markov chain Monte Carlo technique, and the other is the simulated maximum likelihood method based on the Monte Carlo likelihood.This paper examines a quasi-maximum likelihood method based on the Kalman filer.Especially, this paper compares efficiency of the estimator for the simple RSV model.As asymmetry, long memory, and heavy-tailed distributions are three important features for modeling volatility, the paper introduces various RSV models accommodating these structures, and gives details of the estimation methods based on the Kalman filter.The paper reports empirical results for the various RSV model using stock market indices of U.S., U.K., and Japan.

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.

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.

Parametric inference based on empirically estimable divergence is becoming popular. This paper focuses on the divergence with affine invariance as well as empirical estimability. Under some assumptions, we can show that the divergence with these two properties is essentially equivalent to the Hölder divergence. We discuss an intersection between Hölder divergence and well-known Bregman divergence, which becomes a simple divergence with only two parameters. We also consider the parametric inference based on Hölder divergence using an enlarged model. This idea enables us to estimate the outlier ratio as well as the model parameter. In addition, the resulting parameter estimate is based on the γ-divergence, so that the parameter estimate has various useful properties, because the γ-divergence is known as a very useful divergence in robust statistics.

Finding the unbiasedness or biasedness of test statistics is important in testing a hypothesis. The unbiasedness or biasedness of the generalized Wilcoxon rank-sum test and the Jonckheere-Terpstra-type test are investigated. Deriving the exact critical value of the test statistic can be difficult when the sample sizes are increasing. In this situation, an approximation method to the distribution function of the test statistic can be useful with a higher order moment. We derive the expressions for the moment generating function of a linear rank test and a combination of two linear rank statistics. The accuracy of various approximations to the probability of various statistics are investigated. The normal approximation, the Edgeworth expansion, the saddlepoint approximation and the moment-based approximation with an adjusted specific distributional polynomial are used to evaluate the upper tail probability for various nonparametric tests.

The saddlepoint approximations introduced by Daniels (1954) has been used as a simple and useful way for inverting the characteristic function to corresponding p.d.f. However, nowadays the ability of the computing environment enables us to calculate the integration such as Lévy’s inversion formula that includes complex numbers. We shall compare the saddlepoint method with the formula by through some numerical examples. Although the accuracy of the former is inferior to the latter, saddlepoint itself has an inversion formula to get exact p.d.f. Moreover, it naturally explains the performance of the asymptotic normality of a statistics (Takeuchi (2013, 2014)). This is demonstrated when we evaluate the asymptotic normality of the kernel-type density estimator at each point.

This article consists of two parts. In Part I, we briefly summarize some results in three kinds of optimization problems, which have been obtained through our many years' study. More specifically, these are concerned with the problems on maximum likelihood estimation of some parameters, on optimization of correlation with a quadratic constraint, and on optimum stratification. Especially for the stabilities of those optimal solutions, some additional examinations are investigated in this study. In Part II, miscellaneous problems of statistical education in Japan today are pointed out, and some discussion on the direction to be developed is given. We also show some action plans and some proposals.