Integro-difference equations (IDEs) provide a flexible framework for dynamic modeling of spatio-temporal data. The choice of kernel in an IDE model relates directly to the underlying physical process modeled, and it can affect model fit and predictive accuracy. We introduce Bayesian non-parametric methods to the IDE literature as a means to allow flexibility in modeling the kernel. We propose a mixture of normal distributions for the IDE kernel, built from a spatial Dirichlet process for the mixing distribution, which can model kernels with shapes that change with location. This allows the IDE model to capture non-stationarity with respect to location and to reflect a changing physical process across the domain. We address computational concerns for inference that leverage the use of Hermite polynomials as a basis for the representation of the process and the IDE kernel, and incorporate Hamiltonian Markov chain Monte Carlo steps in the posterior simulation method. An example with synthetic data demonstrates that the model can successfully capture location-dependent dynamics. Moreover, using a data set of ozone pressure, we show that the spatial Dirichlet process mixture model outperforms several alternative models for the IDE kernel, including the state of the art in the IDE literature, that is, a Gaussian kernel with location-dependent parameters.

In this paper the authors show how it is possible to establish a common structure for the exact distribution of the main likelihood ratio test (LRT) statistics used in the complex multivariate normal setting. In contrast to what happens when dealing with real random variables, for complex random variables it is shown that it is possible to obtain closed-form expressions for the exact distributions of the LRT statistics to test independence, equality of mean vectors and the equality of an expected value matrix to a given matrix. For the LRT statistics to test sphericity and the equality of covariance matrices, cases where the exact distribution has a non-manageable expression, easy to implement and very accurate near-exact distributions are developed. Numerical studies show how these near-exact distributions outperform by far any other available approximations. As an example of application of the results obtained, the authors develop a near-exact approximation for the distribution of the LRT statistic to test the equality of several complex normal distributions.

Elastic solid antennas are considered. It is shown that many body coherence effects lead to cross sections for pulses, much larger than earlier estimates. For monochromatic continuous signals, the new approach gives the same cross sections as derived in 1960.

A new method for data recording and analysis is proposed. This gives bandwidths several orders larger than are available by recording the output of an optimal filter.

Means are suggested for cascading half acoustic wavelength antennas to give increased cross sections.

Very low temperatures offer methods for selection of antenna quantum states, which imply that the signal to noise ratio can be increased beyond any presently conceived limit.

Multilevel modeling is often used in the social sciences for analyzing data that has a hierarchical structure, e.g., students nested within schools. In an earlier study, we investigated the performance of various prediction rules for predicting a future observable within a hierarchical data set (Afshartous & de Leeuw, 2004). We apply the multilevel prediction approach to the NELS:88 educational data in order to assess the predictive performance on a real data set; four candidate models are considered and predictions are evaluated via both cross-validation and bootstrapping methods. The goal is to develop model selection criteria that assess the predictive ability of candidate multilevel models. We also introduce two plots that 1) aid in visualizing the amount to which the multilevel model predictions are “shrunk” or translated from the OLS predictions, and 2) help identify if certain groups exist for which the predictions are particularly good or bad.

Periodic and aperiodic solutions of the Burgers equation $$u_t + uu_x=\mu u_{xx}, \ \mu > 0,$$ are studied in this paper. A harmonic analysis of the solutions is carried out and the form of the spectrum is estimated for large time. Corresponding estimates of energy decay are also made, In Burgers’ work on this equation. the case in which $$\mu \downarrow 0$$ with t fixed, and one then lets t→∞, is studied. In our investigation, a fixed value of μ > 0 is taken and then one lets t→∞. A similar analysts is also carried out for an irrotaticnal solulion of a similar 3-dimensionat system of equations. For large time and moderate wavenumbers there is. to the first order. a drift of spectral mass from low wavenumbers to higher wavenumbers. Comments are also made on the asymptotic distribution of a class of random solutions.

Large published classifications typically consist of sets (called taxa) hierarchically arranged according to taxonomic rank. A statistical survey of 23 such classification reveals the following distinctive properties. The pattern of mandatory and optional taxonomic ranks is similar to a Guttman scale. Mean taxon size (defined as the number of next-lower-rank taxa per higher-rank taxon) is a U-shaped function of mandatory rank, and averages about seven across ranks with no significant differences between classifications. The variability of taxon size is a decreasing function of mandatory rank. The generality of these properties across classifications suggests that they are determined by the psychology of the classification process. In contrast, there are significant differences between classifications in the variability of taxon size and in the prevalence of optional ranks, both of which are greater in biological than in nonbiological classifications. These differences may reflect the nature of the materials classified.

Asymptotic expansions are established for the power of distributionfree tests in the two-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann for distributionfree tests with respect to their parametric competitors and for the estimators of shift associated with these tests.

In this article, we propose and study a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and the nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both the proposed EM-type algorithms preserve the asymptotic ascent property. A generalized likelihood ratio test is proposed for semiparametric inferences. We prove that the test follows an asymptotic $$\chi ^2$$ -distribution under the null hypothesis, which is independent of the nuisance parameters. A simulation study and two real data examples have been conducted to demonstrate the finite sample performance of the proposed model.