George Woodworth Dec 13, 1999 (Draft please send comments to [email protected]) 1. Background Speech Articulation Data The data in Figure 1 were obtained by asking 51 subjects ranging in age from 8 to 73 years to track, using jaw movements alone, a dot moving sinusoidally in one dimension at .6 Hz on a video monitor. Their jaw movements were captured electronically by means of strain g...

Consider an unknown distribution with a symmetric unimodal density and the induced location-scale family. We study confidence intervals for the location parameter based on Student’s t-statistic, and we conjecture that the uniform distribution is least favorable in that it leads to confidence intervals that are largest given their coverage probability, provided the nominal confidence level is la...

Unimodal (i.e. single-humped) permutations may be decomposed into a product of disjoint cycles. Some enumerative results concerning their cyclic structure — e.g. 23 of them contain fixed points — are given. We also obtain in effect a kind of combinatorial universality for continuous unimodal maps, by severely constraining the possible ways periodic orbits of any such map can nestle together. Bu...

We discuss a robust data sharpening method for rendering a standard kernel estimator, with a given bandwidth, unimodal. It has theoretical and numerical properties of the type that one would like such a technique to enjoy. In particular, we show theoretically that, with probability converging to 1 as sample size diverges, our technique alters the kernel estimator only in places where the latter...

The relation between recurrent behavior and the absence of a stable periodic orbit is discussed for unimodal maps. Almost all periodic maps are non-recurrent and almost all non-periodic are recurrent. Still one feels that the critical orbit cannot accumulate to quickly on the critical point, if it wants to avoid an asymptotic periodic behavior. We obtain exponential bounds of this type in terms...

[1] Most existing stochastic models are developed for unimodal porous media that may be well characterized with only the first two statistical moments. However, the distribution of hydraulic properties, such as hydraulic conductivity, may possess a multiplicity of modes; thus the first two moments may not be adequate to characterize properties of such porous media. In turn, the stochastic model...