Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Fronts with continuous waiting-time distributions: Theory and application to virus infections

We generalize to arbitrary waiting-time distributions some results which were previously derived for discrete distributions. We show that for any two waiting-time distributions with the same mean delay time, that with higher dispersion will lead to a faster front. Experimental data on the speed of virus infections in a plaque are correctly explained by the theoretical predictions using a Gaussian delay-time distribution, which is more realistic for this system than the Dirac delta distribution considered previously [J. Fort and V. Méndez, Phys. Rev. Lett.89, 178101 (2002)]

Consumer valuation of energy-saving features of residential air conditioners with hedonic and choice models

The promotion of energy-efficient appliances is necessary to reduce the energetic and environmental burden of the household sector. However, many studies have reported that a typical consumer underestimates the benefits of energy-saving investment on the purchase of household electric appliances. To analyze this energy-efficiency gap problem, many scholars have estimated implicit discount rates that consumers use for energy-consuming durables. Although both hedonic and choice models have been used in previous studies, a comparison between two models has not yet been done. This study uses point of sale data about Japanese residential air conditioners and estimates implicit discounts rates with both hedonic and choice models. Both models demonstrate that a typical consumer underinvests in energy efficiency. Although choice models estimate a lower implicit discount rate than hedonic models, the latter models estimate the values of other product characteristics more consistently than choice models.