$${\mathcal{Q}}$$-anonymous social welfare relations on infinite utility streams

This paper studies a class of social welfare relations (SWRs) on the set of infinite utility streams. In particular, we examine the SWRs satisfying -Anonymity, an impartiality axiom stronger than Finite Anonymity, as well as Strong Pareto and a certain equity axiom. First, we characterize the extension of the generalized Lorenz SWR by combining -Anonymity with Strong Pareto and Pigou–Dalton Equity. Second, we replace Pigou–Dalton Equity with Hammond Equity for characterizing the extended leximin SWR. Third, we give an alternative characterization of the extended utilitarian SWR by substituting Incremental Equity for Pigou–Dalton Equity.     

Relationships between muscle strength and multi-channel surface EMG parameters in eighty-eight elderly

Background

Since age-related muscle strength loss cannot be explained solely by muscle atrophy, other determinants would also contribute to muscle strength in elderly. The present study aimed to clarify contribution of neuromuscular activation pattern to muscle strength in elderly group. From 88 elderlies (age: 61~?83 years), multi-channel surface electromyography (EMG) of the vastus lateralis muscle was recorded with two-dimensional 64 electrodes during isometric submaximal ramp-up knee extension to assess neuromuscular activation pattern. Correlation analysis and stepwise regression analysis were performed between muscle strength and the parameters for signal amplitude and spatial distribution pattern, i.e., root mean square (RMS), correlation coefficient, and modified entropy of multi-channel surface EMG.

Results

There was a significant correlation between muscle strength and RMS (r =?0.361, p =?0.001) in the elderly. Muscle thickness (r =?0.519, p <?0.001), RMS (r =?0.288, p?=?0.001), and normalized RMS (r =?0.177, p =?0.047) were selected as major determinants of muscle strength in stepwise regression analysis (r?=?0.664 in the selected model).

Conclusion

These results suggest that inter-individual difference in muscle strength in elderly can be partly explained by surface EMG amplitude. We concluded that neuromuscular activation pattern is also major determinants of muscle strength on elderly in addition to indicator of muscle volume.

     

On the leximin and utilitarian overtaking criteria with extended anonymity

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.     

Bias reduction of the maximum-likelihood estimator for a conditional Gaussian MA(1) model

In this paper, we consider an estimation for the unknown parameters of a conditional Gaussian MA(1) model. In the majority of cases, a maximum-likelihood estimator is chosen because the estimator is consistent. However, for small sample sizes the error is large, because the estimator has a bias of O(n^{? 1}). Therefore, we provide a bias of O(n^{? 1}) for the maximum-likelihood estimator for the conditional Gaussian MA(1) model. Moreover, we propose new estimators for the unknown parameters of the conditional Gaussian MA(1) model based on the bias of O(n^{? 1}). We investigate the properties of the bias, as well as the asymptotical variance of the maximum-likelihood estimators for the unknown parameters, by performing some simulations. Finally, we demonstrate the validity of the new estimators through this simulation study.     

Estimating the case fatality rate using a constant cure-death hazard ratio

The case fatality rate is an important indicator of the severity of a disease, and unbiased and accurate estimates of it during an outbreak are important in the study of epidemic diseases, including severe acute respiratory syndrome (SARS). In this paper, estimation methods are developed using a constant cure-death hazard ratio. A semiparametric model is presented, in which the cure-death hazard ratio is a parameter of interest, and a profile likelihood-based technique is proposed for estimating the case fatality rate. An extensive simulation was carried out to investigate the performance of this technique for small and medium sample sizes, using both summary and individual data. The results show that the performance depends on the model validity but is not heavily dependent on the sample size. The method was applied to summary SARS data obtained from Hong Kong and Singapore.