31,763 research outputs found
A Kolmogorov-Smirnov type test for shortfall dominance against parametric alternatives
This paper proposes a Kolmogorov-type test for the shortfall order (also known in the literature as the right-spread or excess-wealth order) against parametric alternatives. In the case of the null hypothesis corresponding to the Negative Exponential distribution, this provides a test for the new better than used in expectation (NBUE) property. Such a test is particularly useful in reliability applications as well as duration and income distribution analysis. The theoretical properties of the testing procedure are established. Simulation studies reveal that the test proposed in this paper performs well, even with moderate sample sizes. Applications to real data, namely chief executive officer (CEO) compensation data and flight delay data, illustrate the empirical relevance of the techniques described in this paper.Right-spread order; Excess-wealth order; New better than used in expectation; Bootstrap; Reliability; CEO compensation; Flight delay
Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient
In this paper we study the distribution function of the
estimators , which optimise the least-squares fitting of the diffusion coefficient
of a single -dimensional Brownian trajectory . We pursue
here the optimisation further by considering a family of weight functions of
the form , where is a time lag and
is an arbitrary real number, and seeking such values of for
which the estimators most efficiently filter out the fluctuations. We calculate
exactly for arbitrary and arbitrary spatial dimension
, and show that only for the distribution
converges, as , to the Dirac delta-function centered at
the ensemble average value of the estimator. This allows us to conclude that
only the estimators with possess an ergodic property, so that the
ensemble averaged diffusion coefficient can be obtained with any necessary
precision from a single trajectory data, but at the expense of a progressively
higher experimental resolution. For any the distribution
attains, as , a certain limiting form with a finite variance,
which signifies that such estimators are not ergodic.Comment: 27 pages, 5 figure
The Complexity of Human Walking: A Knee Osteoarthritis Study
This study proposes a framework for deconstructing complex walking patterns to create a simple principal component space before checking whether the projection to this space is suitable for identifying changes from the normality. We focus on knee osteoarthritis, the most common knee joint disease and the second leading cause of disability. Knee osteoarthritis affects over 250 million people worldwide. The motivation for projecting the highly dimensional movements to a lower dimensional and simpler space is our belief that motor behaviour can be understood by identifying a simplicity via projection to a low principal component space, which may reflect upon the underlying mechanism. To study this, we recruited 180 subjects, 47 of which reported that they had knee osteoarthritis. They were asked to walk several times along a walkway equipped with two force plates that capture their ground reaction forces along 3 axes, namely vertical, anterior-posterior, and medio-lateral, at 1000 Hz. Data when the subject does not clearly strike the force plate were excluded, leaving 1â3 gait cycles per subject. To examine the complexity of human walking, we applied dimensionality reduction via Probabilistic Principal Component Analysis. The first principal component explains 34% of the variance in the data, whereas over 80% of the variance is explained by 8 principal components or more. This proves the complexity of the underlying structure of the ground reaction forces. To examine if our musculoskeletal system generates movements that are distinguishable between normal and pathological subjects in a low dimensional principal component space, we applied a Bayes classifier. For the tested cross-validated, subject-independent experimental protocol, the classification accuracy equals 82.62%. Also, a novel complexity measure is proposed, which can be used as an objective index to facilitate clinical decision making. This measure proves that knee osteoarthritis subjects exhibit more variability in the two-dimensional principal component space
The mechanisms of spatial and temporal earthquake clustering
The number of earthquakes as a function of magnitude decays as a power law.
This trend is usually justified using spring-block models, where slips with the
appropriate global statistics have been numerically observed. However,
prominent spatial and temporal clustering features of earthquakes are not
reproduced by this kind of modeling. We show that when a spring-block model is
complemented with a mechanism allowing for structural relaxation, realistic
earthquake patterns are obtained. The proposed model does not need to include a
phenomenological velocity weakening friction law, as traditional spring-block
models do, since this behavior is effectively induced by the relaxational
mechanism as well. In this way, the model provides also a simple microscopic
basis for the widely used phenomenological rate-and-state equations of rock
friction.Comment: 7 pages, 10 figures, comments welcom
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