On the distribution of quadratic functionals of the ordinary and fractional Brownian motions

In this paper we discuss some distributional properties of quadratic functionals of the ordinary and fractional Brownian motions (fBms). As far as the ordinary Brownian motion (Bm) is concerned, those properties have been established extensively. A transition from the Bm to the fBm is not straightforward. Some difficulties associated with dealing with the fBm are explained, and a way to solving the problem is indicated, and some conjectures are given.     

Who Gets an Early Education? Family Income and the Enrollment of Three‐ to Five‐Year‐Olds from 1968 to 2000*

Objectives. Has inequality in access to early education been growing or lessening over time? Methods. Using the October Current Population Survey education supplement from 1968 to 2000, we look at three‐, four‐, and five‐year‐olds' enrollment in early education—including center‐based care, Head Start, nursery school, prekindergarten, and kindergarten. Results. Our analysis shows a strong link between family income and early education enrollment for three‐ and four‐year‐olds, especially when we compare the bottom two and the top two income groups. These differences remain even after controlling for a large variety of factors, including race/ethnicity, maternal employment, family structure, and parental education. Conclusions. Inequality in early education by income group varies by age of child: it is most pronounced for three‐year‐olds, who have been the least likely to benefit from public early childhood education programs; it has diminished in the past decade for four‐year‐olds, who have been increasingly likely to have access to public prekindergarten programs; and it has all but disappeared for the five‐year‐olds, who now largely attend public kindergarten. This pattern suggests a potentially important role for public policy in closing the gap in early education between children of different income groups.     

Oligarchy for Social Choice Correspondences and Strategy-Proofness

We study the existence of a group of individuals which has some decisive power for social choice correspondences that satisfy a monotonicity property which we call modified monotonicity. And we examine the relation between modified monotonicity and strategy-proofness of social choice correspondences according to the definition by Duggan and Schwartz (2000). We will show mainly the following two results. (1) Modified monotonicity implies the existence of an oligarchy. An oligarchy is a group of individuals such that it has some decisive power (semi-decisiveness), and at least one of the most preferred alternatives of every its member is always chosen by any social choice correspondence. (2) Strategy-proofness of social choice correspondences is equivalent to modified monotonicity.     

Positive Feedback Model for City Vitalization

Abstract  In the present study, we first attempt to construct a model for the dynamics of city images, in which intra- and intercity communications promote the joint possession of city images by residents and the establishment of a city identity. It is suggested that community spirit, which emerges strongly associated with city identity, urges citizens to voluntarily take part in a city's cultural events. The voluntary participation of citizens may change various aspects of a city's functions and physical structure, and as a result the city becomes vitalized in a bottom-up way. Based on this model, we propose a new planning method to facilitate city vitalization as a substitute for hardware-oriented planning. Finally, to ascertain the effectiveness of the new planning method, we focus on Iida City, which has recently successfully established its identity as a puppet drama town.     

Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods

Tanaka (1988) lias derived the influence functions, which are equivalent to the perturbation expansions up to linear terms, of two functions of eigenvalues and eigenvectors of a real symmetric matrix, and applied them to principal component analysis. The present paper deals with the perturbation expansions up to quadratic terms of the same functions and discusses their application to sensitivity analysis in multivariate methods, in particular, principal component analysis and principal factor analysis. Numerical examples are given to show how the approximation improves with the quadratic terms.     

A possible discrepancy between the exposed and the whole population depending on range-size and trap-spacing in vole populations

Conclusion From a field study for the vole population (Clethrionomys rufocanus) in Hokkaido in the late summer of 1965, it has been proved that the range length may decrease from 25 to 18 m by the gross along with the rise from 20 to 100 in the density level per acre, and hence that an appreciable discrepancy, due to underestimation, may be produced in estimates of the exposed as compared to the whole population at an outbreaking density as high as 100 on a plan with trap-spacing 10 m. In consideration of this together with my preceding results, the strict terms that we may enough approximate the whole one by estimating the exposed seem likely to be that the ratio of range radius to trap spacing, supposing a range is circular, should be near 2 or more at either ordinary or outbreaking densities, to say in the concrete, that the trap spacing as close as 5 m or so in grid is desirable with this vole, perhaps with most other voles.     

The Changing Roles of NGOs in Nepal: Promoting Emerging Rights-Holder Organizations for Inclusive Aid

This article examines the unique roles of NGOs with special attention to the changing socio-political contexts of NGOs in terms of their partnerships with Rights-Holder Organizations (RHOs), which claim the rights of particular groups of excluded population. It reviews an example of the NGO working with RHOs in Nepal. NGO relationships with RHOs are delicate and not always equitable due to their different backgrounds and expertise. NGOs, comprising mostly people who are not members of the rights-holding groups, use their expertise to work for others over fixed periods, whilst RHOs work for their own constituencies through movements. Until the 1990s, NGOs supported so-called ‘beneficiaries’ who were members of excluded groups whose rights were being denied. Today, RHOs are formed directly by excluded groups. Some NGOs are trying to change their role to become promoters for RHOs, whilst others remain as their proxies, which merely creates an extra layer between RHOs and donors. The article attempts to prove that building equitable relationships between NGOs and RHOs is possible if NGOs have professionalism, expertise in capacity development and a readiness to become more inclusive. Though there are still several challenges ahead, such efforts by NGOs make it possible to change funding flows for RHOs and contribute to inclusive aid.     

Restricted mean survival time as a summary measure of time‐to‐event outcome

Many clinical research studies evaluate a time‐to‐event outcome, illustrate survival functions, and conventionally report estimated hazard ratios to express the magnitude of the treatment effect when comparing between groups. However, it may not be straightforward to interpret the hazard ratio clinically and statistically when the proportional hazards assumption is invalid. In some recent papers published in clinical journals, the use of restricted mean survival time (RMST) or τ ‐year mean survival time is discussed as one of the alternative summary measures for the time‐to‐event outcome. The RMST is defined as the expected value of time to event limited to a specific time point corresponding to the area under the survival curve up to the specific time point. This article summarizes the necessary information to conduct statistical analysis using the RMST, including the definition and statistical properties of the RMST, adjusted analysis methods, sample size calculation, information fraction for the RMST difference, and clinical and statistical meaning and interpretation. Additionally, we discuss how to set the specific time point to define the RMST from two main points of view. We also provide developed SAS codes to determine the sample size required to detect an expected RMST difference with appropriate power and reconstruct individual survival data to estimate an RMST reference value from a reported survival curve.     

Private provision of public goods between families

We consider a two-stage voluntary provision model where individuals in a family contribute to a pure public good and/or a household public good, and the parent makes private transfers to her own child. We show not only that Warr’s neutrality holds, regardless of the different timings of parent-to-child transfers, but also that there is a continuum of Nash equilibria which individuals’ contributions and parental transfers are indeterminate, although the allocation of each’s private consumption and total public good provision is uniquely determined. Furthermore, impure altruism or productivity difference in supplying public goods may not break our results above.     

ANALYZING INDUSTRY‐LEVEL VULNERABILITY BY PREDICTING FINANCIAL BANKRUPTCY

This study introduces a novel framework for building company bankruptcy models and a methodology for assessing the vulnerability of industrial economic activities. We consider the identification of bankruptcy as a classification problem and assume that bankruptcy criteria differ across industries. We build highly accurate industry bankruptcy models by constructing separate models for each industry. We also propose a method of analyzing the vulnerability of industrial economic activities in various countries and industries using new indicators we call “expected potential loss,” which we obtain using the predicted likelihood of bankruptcy and company information. (JEL G0, C0)