Constrained ordination methods aims at finding an environmental gradient along which the species abundances are maximally separated. The species response functions, which describe the expected abundance as a function of the environmental score, are according to the ecological fundamental niche theory only meaningful if they are bell-shaped. Many classical model-based ordination methods, however...

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping whe...

As a technical supplement to Zhu and Zhang (2004), we give detailed information on how to establish asymptotic theory for both maximum likelihood estimate and maximum modified likelihood estimate in mixture regression models. Under specific and reasonable conditions, we show that the optimal convergence rate of n− 1 4 for estimating the mixing distribution is achievable for both the maximum lik...

The likelihood ratio test statistic G(2)(dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly specified. Yet, this statistic is often used in appli...

Automated variable selection procedures, such as backward elimination, are commonly employed to perform model selection in the context of multivariable regression. The stability of such procedures can be investigated using a bootstrap-based approach. The idea is to apply the variable selection procedure on a large number of bootstrap samples successively and to examine the obtained models, for ...

Consider a particle moving on the surface of the unit sphere in R and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for various characteristics of the process including expected travel time to a cap, the limiting distribution...

The most widely used measure of segregation is the so-called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if ...

D. Davis and W. C. Follette (2002) purport to show that when "the base rate" for a crime is low, the probative value of "characteristics known to be strongly associated with the crime ... will be virtually nil." Their analysis rests on the choice of an arbitrary and inopposite measure of the probative value of evidence. When a more suitable metric is used (e.g., a likelihood ratio), it becomes ...

We introduce a nearly automatic procedure to locate and count the quantum dots in images of kinesin motor assays. Our procedure employs an approximate likelihood estimator based on a two-component mixture model for the image data; the first component has a normal distribution, and the other component is distributed as a normal random variable plus an exponential random variable. The normal comp...

The union-intersection principle yields a class of multiple comparison tests that include the classical Scheffé tests for analysis of variance, and are easily applied to any likelihood ratio test. Examples are given.