An impossibility theorem for matching problems

This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to matching problems. Alcalde and Barberá (Econ Theory 4:417–435, 1994) and Sönmez (Econ Des 1:365–380, 1994) show that efficient and individually rational matching rules are manipulable. We pursue the possibility of strategy-proof matching rules by relaxing efficiency to the weaker condition of respect for unanimity. First, we prove that a strategy-proof rule exists that is individually rational and respects unanimity. However, this rule is unreasonable in the sense that mutually best pairs of agents are matched on only rare occasions. In order to explore the possibility of better matching rules, we introduce a natural condition of “respect for 2-unanimity.” Respect for 2-unanimity states that a mutually best pair of agents should be matched, and an agent wishing to being unmatched should be unmatched. Our second result is negative. Secondly, we prove that no strategy-proof rule exists that respects 2-unanimity. This result implies Roth (Math Oper Res 7:617–628, 1962; J Econ Theory 36:277–288, 1985) showing that stable rules are manipulable.     

Nonlinear regression modeling via the lasso-type regularization

We consider the problem of constructing nonlinear regression models with Gaussian basis functions, using lasso regularization. Regularization with a lasso penalty is an advantageous in that it estimates some coefficients in linear regression models to be exactly zero. We propose imposing a weighted lasso penalty on a nonlinear regression model and thereby selecting the number of basis functions effectively. In order to select tuning parameters in the regularization method, we use a deviance information criterion proposed by Spiegelhalter et al. (2002), calculating the effective number of parameters by Gibbs sampling. Simulation results demonstrate that our methodology performs well in various situations.     

Use of non-normality in structural equation modeling: Application to direction of causation

Structural equation modeling (SEM) typically utilizes first- and second-order moment structures. This limits its applicability since many unidentified models and many equivalent models that researchers would like to distinguish are created. In this paper, we relax this restriction and assume non-normal distributions on exogenous variables. We shall provide a solution to the problems of underidentifiability and equivalence of SEM models by making use of non-normality (higher-order moment structures). The non-normal SEM is applied to finding the possible direction of a path in simple regression models. The method of (generalized) least squares is employed to estimate model parameters. A test statistic for examining a fit of a model is proposed. A simulation result and a real data example are reported to study how the non-normal SEM approach works empirically.     

Effects of 10-week walking and walking with home-based resistance training on muscle quality,muscle size,and physical functional tests in healthy older individuals

Background

Older individuals have been shown to present muscle atrophy in conjunction with increased fat fraction in some muscles. The proportion of fat and connective tissue within the skeletal muscle can be estimated from axial B-mode ultrasound images using echo intensity (EI). EI was used to calculate the index of muscle quality. Walking, home-based weight-bearing resistance training, and its combinations are considered simple, easy, and practical exercise interventions for older adults. The purpose of this study was to quantify the effects of walking and walking with home-based resistance training on muscle quality of older individuals.

Methods

Thirty-one participants performed walking training only (W-group; 72?±?5?years) and 33 participants performed walking and home-based resistance training (WR-group; 73?±?6?years). This study was a non-randomized controlled trial with no control group. All participants were instructed to walk 2 or 3 sets per week for 10?weeks (one set: 30-min continuous walking). In addition, the WR-group performed home-based weight-bearing resistance training. EI was measured as a muscle quality index using axial B-mode ultrasound images of the rectus femoris and vastus lateralis of the mid-thigh. We further averaged these parameters to obtain the EI of the quadriceps femoris (QF). Participants further performed five functional tests: sit-ups, supine up, sit-to-stand, 5-m maximal walk, and 6-min walk.

Results

QF EI was significantly decreased in both groups after training (W-group 69.9?±?7.4?a.u. to 61.7?±?7.0?a.u., WR-group 64.0?±?9.5?a.u. to 51.1?±?10.0?a.u.; P?<?0.05), suggesting improved muscle quality. QF EI was further decreased in the WR-group compared with the W-group. The sit-up test in both groups and the sit-to-stand and 5-m maximal walk tests in the W-group were significantly improved after training.

Conclusion

These results suggest that training-induced stimulation is associated with a decrease in EI in some thigh regions. Furthermore, the addition of home-based resistance training to walking would be effective for a greater reduction of EI.