We propose a formal method to test stationarity for spatial point processes. The proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity. We show that the resulting test statistic converges in distribution to a functional of a two-dimensional Brownian motion. To conduct the test, we compare the calculated s...

In this paper, we introduce a Goodness-of-Fit test for the Multivariate Exponential Power (MEP) distribution, a multivariate extension of the Generalized Gaussian, which has recently gained considerable interest as a model for wavelet coefficients in the context of color image retrieval and spread-spectrum watermarking. We present a size and power study of this test and show Goodness-of-Fit res...

For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized li...

We introduce a formal testing procedure to assess the goodness-of-fit of a fitted inhomogeneous spatial Poisson process model. Our method is based on a discrepancy measure function Dc(t; θ̂) that is constructed by using residuals obtained from the fitted model. We derive the asymptotic distributional properties of Dc(t; θ̂) and then develop a test statistic based on these properties. Our test sta...

Bootstrap is the standard method in the spatial scan test. However, because the spatial scan statistic lacks theoretical properties, its development and connection to mainstream statistics has been limited. Using the methods of empirical processes with a few weak regularity conditions, the limiting distribution of the spatial scan statistic, which can provide a theoretical basis for the spatial...

We study statistical methods to detect cancer genes that are over- or down-expressed in some but not all samples in a disease group. This has proven useful in cancer studies where oncogenes are activated only in a small subset of samples. We propose the outlier robust t-statistic (ORT), which is intuitively motivated from the t-statistic, the most commonly used differential gene expression dete...

Background Cohen's Kappa is the most used agreement statistic in literature. However, under certain conditions, it is affected by a paradox which returns biased estimates of the statistic itself. Objective The aim of the study is to provide sufficient information which allows the reader to make an informed choice of the correct agreement measure, by underlining some optimal properties of Gwet...

We review three recently proposed scan statistic methods for multivariate pattern detection. Each method models the relationship between multiple observed and hidden variables using a Bayesian network structure, drawing inferences about the underlying pattern type and the affected subset of the data. We first discuss the multivariate Bayesian scan statistic (MBSS) proposed by Neill and Cooper (...

BACKGROUND The spatial scan statistic proposed by Kulldorff has been applied to a wide variety of epidemiological studies for cluster detection. This scan statistic, however, uses a circular window to define the potential cluster areas and thus has difficulty in correctly detecting actual noncircular clusters. A recent proposal by Duczmal and Assunção for detecting noncircular clusters is shown...

In the article the logistic regression modeling method was proposed to evaluate the innovativeness of 207 inquired enterprises of Lublin Region. Single and multiequation models describing the process of introduction in 2002 and the plans of introduction in 2003 of the technological, organizational and product innovations were built. Checked with many indicators (Pearson chi – squared statistic,...