Several least-squares problems related to the Hodrick–Prescott filtering

The Hodrick–Prescott (HP) filtering is frequently used in macroeconometrics to decompose time series, such as real gross domestic product, into their trend and cyclical components. Because the HP filtering is a basic econometric tool, it is necessary to have a precise understanding of the nature of it. This article contributes to the literature by listing several (penalized) least-squares problems that are related to the HP filtering, three of which are newly introduced in the article, and showing their properties. We also remark on their generalization.     

A small but practically useful modification to the Hodrick–Prescott filtering: A note

The Hodrick–Prescott (HP) filtering is widely applied to decompose macroeconomic time series, such as real Gross Domestic Product, into cyclical and trend components. This paper presents a small but practically useful modification to this approach. The reason why this modified filtering is of practical use is that it provides not only identical trend estimates as the HP filtering but also extrapolations of the trend. We provide a proof based on a ridge regression representation of the modified HP filtering. This is mainly because it enhances our understanding of the approach.     

The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression

The Frisch–Waugh–Lovell (FWL) (partitioned regression) theorem is essential in regression analysis. This is partly because it is quite useful to derive theoretical results. The lasso regression and the ridge regression, both of which are penalized least-squares regressions, have become popular statistical techniques. This article describes that the FWL theorem remains valid for these penalized least-squares regressions. More precisely, we demonstrate that the covariates corresponding to unpenalized regression parameters in these penalized least-squares regression can be projected out. Some other results related to the FWL theorem in such penalized least-squares regressions are also presented.     

Construction of the integrated model for practical career support to the professional athletes

Recently, along with the enhancement of the argument for career of athletes, many researchers who major in sports psychology focus mainly on athletic retirement, a coordination of transitions in sport or and outside sport, social support and professional assistance in career transition, in the context of the second career concerning to professional athletes in Japan. However, when it comes to career transition of professional athletes, it is necessary to consider "career" from the whole perspectives of human life. Therefore, the purpose of this study is to clarify the career transition of professional athletes by the way of questionnaire and interview survey, which is approached from the view point of industrial/organizational psychology. For this purpose, we implemented the interview survey to professional athletes in 2008. In addition, we carried out the investigation to professional football players (interview survey: 5 players, questionnaire survey: 102 players) in 2009. Consequently, three following findings were led in conclusion. (1)Career intervention to professional athletes should be performed before the turning point of the career (career transition). (2)It is important to assess the career intervention to professional athletes. (3)It is an important stance to watch the processes when professional athletes open up one's career by oneself.     

Interval estimation in discriminant analysis for large dimension

This paper is concerned with the interval estimation for the log odds of the posterior probability that the observation vector belongs to one of two homoscedastic multivariate normal distributions (Π₁ and Π₂). We give the limiting distribution of the unbiased estimator for the log odds as the sample sizes and the dimension jointly tend to infinity, and approximate the confidence interval based on the asymptotic distribution. Small-scale simulations are performed to check the precision of the approximation.     

Japanese Children's Reasoning about Conflicts with Parents

Ninety-five Japanese children (aged 6–12) were interviewed using hypothetical stories to examine their reasoning about parent–child conflicts. Participants were most likely to reject parental authority and to support child's discretion in conflict situations where the parent interfered in the child's personal choice and gave the child commands that violated moral and conventional principles. However, participants were most likely to accept parental authority when the child's wish conflicted with the parent's moral concern. Participants' reasoning was more varied when the child's wish went against the parent's conventional demand. Consistent with their cultural values, participants considered harmonious relationships in evaluating conventional and personal conflicts, but not moral conflicts. Age differences were observed in the endorsement of personal choice. Results suggest that children do not simply act upon their cultural values but also show resistance to parental authority for reasons beyond meeting selfish needs and form differentiated judgments about parent–child conflicts.     

Licensing and training requirements for direct care workers in Japan: what can the United States and Japan learn from each other?

Shortages of direct care workers have been of concern both in the United States and in Japan. This article compares issues surrounding long-term care provisions in the two countries and introduces Japan's unique licensure and certificate system for direct care workers. Japan has established three levels of direct care worker certificates and a direct care licensure, which can be potentially used as a career ladder. Studies show that this system has resulted in different work conditions and benefits between different certificate and licensure levels but had a limited impact on hourly wage and task differentiation. Implications for the United States are also discussed.     

Supersaturated design including an orthogonal base

Recently, many supersaturated designs have been proposed. A supersaturated design is a fractional factorial design in which the number of factors is greater than the number of experimental runs. The main thrust of the previous studies has been to generate more columns while avoiding large values of squared inner products among all design columns. These designs would be appropriate if the probability for each factor being active is uniformly distributed. When factors can be partitioned into two groups, namely, with high and low probabilities of each factor being active, it is desirable to maintain orthogonality among columns to be assigned to the factors in the high-probability group. We discuss a supersaturated design including an orthogonal base which is suitable for this common situation. Mathematical results on the existence of the supersaturated designs are shown, and the construction of supersaturated designs is presented. We next discuss some properties of the proposed supersaturated designs based on the squared inner products.     

Testing Equality of Mean Vectors in Two Sample Problem with Missing Data

Finding the influence of traffic accident on the road is helpful to analyze the characteristics of traffic flow, and take reasonable and effective control measures. Here, the detrended fluctuation analysis method is applied to investigate the complexity of time series in mixed traffic flow with a blockage induced by an accident. As a parameter to depict the long-term evolutionary behavior of the time series in traffic flow, the scaling exponent is analyzed. According to the scaling exponent, it is shown that the traffic flow time series can display long-range correlation characteristics, short-range correlation characteristics, and non-power-law relation in the long-range correlation characteristics, which is strongly dependent on the entering probability of vehicle, the ratio of slow vehicle and the blockage duration time.     

Enriching Surveys with Supplementary Data and its Application to Studying Wage Regression

We consider the problem of supplementing survey data with additional information from a population. The framework we use is very general; examples are missing data problems, measurement error models and combining data from multiple surveys. We do not require the survey data to be a simple random sample of the population of interest. The key assumption we make is that there exists a set of common variables between the survey and the supplementary data. Thus, the supplementary data serve the dual role of providing adjustments to the survey data for model consistencies and also enriching the survey data for improved efficiency. We propose a semi‐parametric approach using empirical likelihood to combine data from the two sources. The method possesses favourable large and moderate sample properties. We use the method to investigate wage regression using data from the National Longitudinal Survey of Youth Study.