Evaluation of multilevel decision trees

The evaluation of decision trees under uncertainty is difficult because of the required nested operations of maximizing and averaging. Pure maximizing (for deterministic decision trees) or pure averaging (for probability trees) are both relatively simple because the maximum of a maximum is a maximum, and the average of an average is an average. But when the two operators are mixed, no simplification is possible, and one must evaluate the maximization and averaging operations in a nested fashion, following the structure of the tree. Nested evaluation requires large sample sizes (for data collection) or long computation times (for simulations).     

Inference about permutation parameter in large samples

The estimation problem of a permutation parameter on the basis of a random sample of increasing size is considered. A necessary and sufficient condition for the existence of an estimator, asymptotically fully efficient for two different distributions families, is derived. We also study the application of this result to cyclic groups of order two and three.     

A computational general equilibrium approach to the shadow pricing of trade restrictions and the adjustment of the exchange rate, with an application to Argentina

A general equilibrium model of an open economy in which there are ad valorem texes on domestic production and export activities, and import activities are subject to both tariffs and quotas is constructed. A domestic monetary asset, foreign exchange, and a corresponding nominal exchange rate are introduced and a numerical example of the model is constructed. The example is solved via the Scarf fixed point algorithm, first with taut quotas and then after having relaxed quotas. Various price indices are then used to guide programs designed to stabilize the trade balance against the quota liberalization. An empirical example, using Argentine data, is carried out to find the quota equivalent of a particular tariff.     

Autism: understanding conceptual processing deficits

Autism is a behavioral diagnosis characterized by a triad of impairment, which includes impaired communication, impaired social skills, and impaired spontaneity. The outward behavior exhibited by people with autism represents a different cognitive processing style than that seen in typical development. Understanding the way people with autism process and store information is important for intervention. The majority of people diagnosed with autism do not have symptoms of mental retardation and need access to mainstream services to work on the problems presented by daily life.     

The interaction of aging and 10 years of racing on ultraendurance running performance

The aim of this study was to examine the interaction between aging and 10 years of racing in endurance runners. Race-time data from 194 runners who had completed 10 consecutive 56-km ultramarathons were obtained. The runners were either 20.5 +/- 0.7, 30.0 +/- 1.0, 39.9 +/- 0.9, or 49.4 +/- 1.0 years old at their first race. Each runner's race speed was determined for each race over the 10 years. Data were analyzed using repeated-measures ANOVA, one-way ANOVA, and independent t tests and showed that performance improved and declined at greater rates for younger runners; younger runners had a greater capacity for improvement than older runners; approximately 4 years were required to reach peak racing speed, regardless of age; it was not possible to compete at peak speed for more than a few years; and the combined effects of 10 years of aging and racing neither improve nor worsen net performance. In conclusion, these data suggest that although these runners showed similar patterns of change in race speed over a 10-year period, the extent of change in performance was greater in younger than in older runners.     

Approximation of power in multivariate analysis

We consider the calculation of power functions in classical multivariate analysis. In this context, power can be expressed in terms of tail probabilities of certain noncentral distributions. The necessary noncentral distribution theory was developed between the 1940s and 1970s by a number of authors. However, tractable methods for calculating the relevant probabilities have been lacking. In this paper we present simple yet extremely accurate saddlepoint approximations to power functions associated with the following classical test statistics: the likelihood ratio statistic for testing the general linear hypothesis in MANOVA; the likelihood ratio statistic for testing block independence; and Bartlett's modified likelihood ratio statistic for testing equality of covariance matrices.