Meta-analysis is a statistical method to summarize quantitative results from a set of published studies. Meta-analysis often assumes that the outcomes of all individual studies have a common mean and estimates the common mean based on the results of each study. On the other hand, meta-analysis sometimes shows an updated estimate of individual study. This paper is a review article for estimation of individual normal means based on pretest estimators using meta-analytic data. New results on the bias, mean squared error, and variance of the pretest estimator are also included in this paper. The use of the R package: meta.shrinkage is also described. An example of the application to eye allergic reaction data during anatomy practice is also reported.

Causality is a fundamental and crucial subject of analysis in many research fields, including statistical science. In the fields of biometrics and econometrics, statistical causal inference has been widely applied. In this paper we first introduce the counterfactual model, initiated by Rubin (1974), and the instrumental variables method proposed by Angrist, Imbens, and Rubin (1996, referred to as AIR) in biometrics and statistics. Next, we explain simultaneous equations and structural equations in econometrics using a simple demand function as an example. We interpret statistical causality using general structural equations and discusses statistical estimation methods for structural equations, including the instrumental variables approach. Since the Ordinary Least Squares (OLS) method is inconsistent in estimating structural equations, alternative methods such as the Wald method, Limited Information Maximum Likelihood (LIML), Two-Stage Least Squares (TSLS), and Generalized Method of Moments (GMM) are discussed with their advantages and disadvantages. Furthermore, we review the historical development of structural equations and presents new findings regarding the instrumental variables estimation method in two-sample. Finally, we explore future challenges in statistical causal analysis in biometrics and econometrics.

Childbirth occurs at a certain stage in life, mainly between the late teens and 40s. The trend of this life event from the distant past may be linked to subsequent changes in lifestyle and health, and may be related to mortality and other outcomes. It is important to take into account the year of birth rather than just the calendar year. Therefore, we estimate the long-term trends in the number of children born to Japanese women according to year of birth. Using the number of children born to wives aged mainly 45–49 from the population census and the national fertility surveys during 1950 and 2021, we obtained the distribution of the number of children born to Japanese women, born between 1890 and 1973, adjusted by the female unmarried rate. Since this distribution of the number of children born is calculated at ve-year intervals, we further conrmed the detailed changes by age-specic fertility rate at one-year intervals.

This paper focuses on the mathematical method which evaluates the completeness for estimation of nationwide cancer incidence in Japan. The information for national cancer incidence is currently reported by the National Cancer Registry, but it was previously estimated based on regional cancer registry. It has been pointed out that regional cancer registry contains registration omissions, which may have provided the underestimate for the national incidence. Then, in this paper, we focus on the statistical method, which is based on binomial regression model with indices of completeness, to estimate the completeness of registration. The method was applied to the 2015 data and estimate the registration rate.

A non-normalized model is a statistical model defined by an unnormalized density, i.e., a density function that does not integrate to one. In machine learning, such models are often referred to as energy-based models. Examples include Markov random fields, distributions on manifolds, and Boltzmann machines. These models allow for flexible data modeling but present challenges for likelihood-based statistical inference due to the presence of an intractable normalization constant. To address this issue, various statistical inference methods that do not require explicit computation of the normalization constant have been developed. In this paper, we introduce two parameter estimation methods for non-normalized models: score matching and noise contrastive estimation. We also discuss recent advancements, such as information criteria and nonlinear independent component analysis, as well as connections to other statistical methods, including shrinkage estimation and bridge sampling.

The function, whose input and output have a one-to-one correspondence, is said to be invertible. This study focuses on the invertibility constraint and reviews recent studies on invertible prediction models. Additionally, as part of our research Okuno and Imaizumi (2024), we discuss how strong the invertibility constraint is compared to existing conditions such as the Lipschitz constraint from the perspective of minimax rates. Furthermore, we introduce a nonparametric invertible estimator and demonstrate that it achieves the minimax optimality.