We examine a test of a nonparametric regression function based on penalized spline smoothing. We show that, similarly to a penalized spline estimator, the asymptotic power of the penalized spline test falls into a small- K or a large-K scenarios characterized by the number of knots K and the smoothing parameter. However, the optimal rate of K and the smoothing parameter maximizing power for tes...

By introducing the asymptotic logarithmic likelihood ratio as a measure of the Markov approximation of arbitrary random fields on a uniformly bounded tree, by constructing a non-negative martingale on a uniformly bounded tree, a class of small deviation theorems of functionals and a class of small deviation theorems of the frequencies of occurrence of states for random fields on a uniformly bou...

We study in this paper some nonparametric inference problems where the nonparametric maximum likelihood estimator (NPMLE) are not well defined. However, if we enlarge the parameter space, the NPMLE will be well defined. We propose to gradually shrink the enlarged parameter space by placing more and more restrictions on the parameter space, producing a sequence of (envelope) estimators. The appr...

We evaluate the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high-dimensional data under a general multivariate model. Data dimension and dependence among components of the multivariate random vector affect the empirical likelihood directly through the trace and the eigenvalues of the covariance matrix. The growth rates to infinity we obtain for th...

This article deals with the problem of testing the hypothesis that q p-variate normal distributions are independent and that their covariance matrices are equal. The exact null distribution of the likelihood ratio statistic when q = 2 is obtained using inverse Mellin transform and the definition of Meijer’s G-function. Results for p = 2, 3, 4 and 5 are given in computable series forms.

Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are invariant to changes in the univariate marginal distributions, rank-based estimators are natural candidates for semiparametric copula estimation. Asymptotic informa...

In this paper, radar detection based on Monte Carlo sampling is studied. Two detectors based on Importance Sampling are presented. In these detectors, called Particle Detector, the approximated likelihood ratio is calculated by Monte Carlo sampling. In the first detector, the unknown parameters are first estimated and are substituted in the likelihood ratio (like &#10the GLRT method). In the s...

It has been assumed that stimulus discrimination in a visual task is performed with fixed attentive effort. Here we show that attention to the same pair of stimuli can be modulated by varying the task difficulty when a task requires the discrimination of only a small number of different stimuli. We used a matching-to-sample paradigm, where a test stimulus is presented after a sample stimulus. W...

ity scale for clinicians is symmetrically skewed in both directions. In primary care, elective surgery, and oncology, clinicians work at the extremes of the probability scale. The time has come to apply the Feynman-Tufte principle to clinical logic, to offer a visual representation of Bayesian logic. Earlier attempts with natural logarithmics do not allow a simple graphic. We teach a scale of l...

The clinical relevance of likelihood ratios (L-values) for revising the physician's diagnostic probabilities has been recognized. However, the calculation of L-values, particularly in the case of quantitative or mixed quantitative-binary test results, raises problems that have not yet been addressed. Based on a very general assumption that yields a simple functional form for the likelihood rati...