Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 3-23

## Semiparametric Estimation under Nonresponse in Survey and Sensitivity Analysis: Application to the 12th Survey of the Japanese National Character

(Department of Economics, Nagoya University)

In recent years, the collection rate for conventional types of surveys such as visit survey with random sampling has been declining. Therefore, a solution for bias due to nonresponse needs to be developed. We formulate the bias due to nonresponse in a survey as “selection bias” in econometrics, and I point out the problems in applying covariate adjustment methods to nonresponse in surveys. In this paper, we propose a semiparametric Bayes model where a latent hidden covariate affect both the response variables and the indicator of nonresponse using Dirichlet process mixtures. By changing some portion of parameters, we can conduct a sensitivity analysis to investigate how much the confidence interval is under a high rate of nonresponse. We apply the proposed method to the 12th survey of the Japanese National Character, and found that the method provides more reasonable confidence intervals, compared to that calculated without any model assumption.

Key words: Dirichlet process mixture model, propensity score, hidden covariate, sociological surveys, covariate adjustment, selection bias.

Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 25-38

## Two-stage Non-response Bias Adjustment Using Variables on the Survey-orienting Character for the Survey on the Japanese National Character

(The Institute of Statistical Mathematics)

The response rate of surveys on the Japanese national character has declined to 51.6%, which is the lowest ever. Although simple proportions among respondents have hitherto been used as population estimators, they will certainly exhibit serious biases in some question items. This paper attempts to reduce these biases by adjusting the estimation weights. The two main reasons for non-response are absence and refusal. Hence, the weights were calibrated in two stages that accounted for each reason. They were calibrated using not only demographic variables, but also variables that measure respondents' attitudes toward the survey in each stage. We consider the latter variables to be those on the survey-orienting character used in this paper. The calibrated estimates differ by ten percentage points at most from the simple proportions. The differences were larger in the calibrated estimates that used variables on the survey-orienting character than in the calibrated estimates that used only the demographic variables. Although we cannot conclude that the estimates are totally free from biases, the calibrated estimates appear to be reasonable, considering the known characteristics of the nonrespondents.

Key words: Non-response, absence, refusal, calibration, variable on the survey-orienting character.

Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 39-59

## Contemporary Japanese Religious Mind—Based on Survey Data from the Japanese National Character and Other Cross-national Surveys

(Faculty of Human Sciences, Toyo Eiwa University)

This paper investigates contemporary Japanese attitudes toward religion by tracing changes in response patterns to questions relating to religion included in various installments of the Japanese National Character Surveys from 1953 to 2008. It also compares these findings to the results of a number of other international comparative surveys. A cohort analysis reveals that the increase in religiosity of the Japanese stems mainly from age effect. To visualize the relationship between religiosity and the importance of the “religious mind” in a broader sense in contemporary Japanese societies, the Quantification III method, incorporating nearly all questions included in the 12$^{\rm th}$ installment of the National Character Survey, was employed. This resulted in a 2-dimensional configuration that displays structural patterns in people's minds. Among other things, this effort demonstrated that while both religiosity and the importance of the religious mind are associated with positive attitudes toward society in general, a view holding that the “religious mind is unimportant” is associated with more negative attitudes toward society. Relationships between religiosity and the importance of the religious mind with other general social attitudes and orientations were also discussed, based on comparisons of results of these analyses after adjusting for differences in the distribution of respondents by age.

Key words: Religious mind, religious faith, structure of Japanese attitudes, comparative social attitude surveys among seven nations, east Asia value surveys, the Asia & Pacific value surveys, quantification method III.

Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 61-82

## Memories of a Statistical Study on the Japanese National Character: Looking Back on 36 Years of Being a Researcher at the Institute of Statistical Mathematics

(Professor Emeritus, The Institute of Statistical Mathematics; Project Professor (April 2007--March 2010), Department of Economics, Hitotsubashi University)

A statistical survey of the Japanese national character was first conducted in 1953 by the Research Committee of the Institute of Statistical Mathematics. Since then, a similar statistical survey has been conducted every five years, totaling twelve surveys. Three major purposes of this research on the Japanese national character are to study Japanese ways of thinking, social survey techniques, and statistical methods for analyzing social survey data. The author worked in this research project from 1973 to 2007, and has published many works on these subjects. The purpose of this paper is to demonstrate typical examples of these works. The topics are concerned with Japanese attitude trends over the period 1953 to 2008, some findings on the Japanese way of thinking, some problems on the reality of field work, the reconstruction of statistics based on Akaike information criterion and so forth.

Key words: Survey of the Japanese national character, values, longitudinal survey, social survey technique, information criteria, Akaike information criterion statistics.

Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 113-126

## Optimal Aggregation of Adjacent Forest Stands through Traditional Spatially Constrained Harvest Scheduling Approach

(The Institute of Statistical Mathematics)
(Graduate School of Life Sciences, Tohoku University)
(Department of Mathematics, Graduate School of Science, Hiroshima University)

Aggregation of small scale forest stands into one management unit has been one of the main issues in improving the management scheme in Japan. This aggregation could reduce the main production cost such as transportation costs by building an efficient road network in the aggregated management unit, where each forest stand is often owned by different forest owners. GIS has been widely and manually used for this purpose because aggregation of forest stands requires geographical information such as adjacency of forest stands. Since aggregation of adjacent forest stands is one of spatially constrained harvest scheduling problems, we formulate this aggregation problem as an adjacency problem within the optimization framework. In order to formulate our adjacency problem, we introduce the concept of a “hyper unit” for a possible aggregated management unit, for which adjacent constraints are assigned to avoid duplication of hyper units for final selection. We demonstrate how hyper units are created and our adjacency problem is solved using a case study in Sagawa forest, Japan.

Key words: Aggregation, forest landscape management, spatial allocation analysis, 0-1 integer programming.

Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 127-130

## A Remark on Projection Estimator

(The Institute of Statistical Mathematics)

We remark that the leading constant of the asymptotic bound for the $L_2$ risk of the projection estimator for a density on $[-\pi, \pi ]$ is $1/\pi$, which does not depend on the true density. In this sense, the projection estimator has a merit that the kernel estimators do not have.

Key words: Density estimation, $L_2$ risk, orthonormal system.

Proceedings of the Institute of Statistical Mathematics Vol. 58, No. 1, 131-135

## Uniform Rate of Convergence of Smoothed Nelson-Aalen Estimator

(The Institute of Statistical Mathematics)

In the multiplicative intensity model for counting processes, Ramlau-Hansen (1983, Ann. Statist.) derived the uniform consistency of the smoothed Nelson-Aalen estimator for the hazard function. We extend this result to the case where the rate of uniform consistency is $o_{P}(n^{-1/2}b_n^{-1})$ where $b_n$ is the bandwidth, by using the weak convergence theory for $\ell^\infty$-valued martingales given by Nishiyama (2000a, Ann. Probab.).

Key words: Kernel estimator, smoothing, Nelson-Aalen estimator, uniform consistency.