Multi-dimensional Goodness-of-Fit Tests for Spectrum Sensing Based on Stochastic Distances

In this paper, we study two multi-dimensional Goodness-of-Fit tests for spectrum sensing in cognitive radios. The multi-dimensional scenario refers to multiple CR nodes, each with multiple antennas, that record multiple observations from multiple primary users for spectrum sensing. These tests, viz., the Interpoint Distance (ID) based test and the h, f distance based tests are constructed based on the properties of stochastic distances. The ID test is studied in detail for a single CR node case, and a possible extension to handle multiple nodes is discussed. On the other hand, the h, f test is applicable in a multi-node setup. A robustness feature of the KL distance based test is discussed, which has connections with Middleton's class A model. Through Monte-Carlo simulations, the proposed tests are shown to outperform the existing techniques such as the eigenvalue ratio based test, John's test, and the sphericity test, in several scenarios.

The form and function of aggressive subtypes: Relations with the goodness of fit between adolescent temperament and parent personality

The current research investigated whether the interaction between adolescent temperament and parent personality, consistent with the goodness of fit perspective, differentially predicted overt (e.g., kicking, punching, insulting) and relational (e.g., gossiping, rumour spreading, ostracising) forms of reactive (e.g., provoked, a response to goal blocking, unplanned and emotional) and proactive (e.g., unprovoked, goal-directed, deliberate and relatively unemotional) aggression. Mothers, fathers and their adolescent child (N = 448, age 10-17) from southern Ontario, Canada filled out questionnaires on adolescent temperament (i.e., frustration, fear, and effortful control) and aggression. Parents reported on their own personality traits (i.e., agreeableness, conscientiousness, and emotional stability). The form and function of aggression not encompassed by the subtype under investigation were controlled in each regression analysis. Consistent with the hypothesis, results indicated that a poor fit between adolescent temperament vulnerabilities and lower parent personality traits, including agreeableness, conscientiousness and emotional stability, was predictive of greater levels of differentiated aggression. For instance, lower father conscientiousness strengthened the relation between higher frustration and reactive overt aggression. Unexpectedly in some cases, temperament risk factors were more strongly associated with aggression subtypes when personality scores were at higher levels, particularly agreeableness and conscientiousness, traits normally considered to be at the optimal end of the dimension. For example, higher father agreeableness strengthened the relation between higher frustration and reactive relational aggression. At the main effects level, low fearfulness was significantly associated with only the overt subtypes of aggression, and unexpectedly, higher frustration and lower effortful control were related to both proactive and reactive subtypes of aggression. A temperamentally vulnerable adolescent was also at greater risk of displaying aggressive behaviour when the father lacked emotional stability, but not the mother. These results are broadly consistent with the prediction that temperament risk factors are more strongly associated with aggression subtypes when an adolescent predisposition does not fit well with parent personality traits. Mechanisms pertaining to stress in the family environment and the fostering of self-regulation abilities are discussed with respect to why a poor fit between temperament and parent personality is predictive of adolescent differentiated aggression.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Being and goodness

The old scholastic principle of the "convertibility" of being and goodness strikes nearly all moderns as either barely comprehensible or plain false. "Convertible" is a term of art meaning "interchangeable" in respect of predication, where the predicates can be exchanged salva veritate albeit not salva sensu: their referents are, as the maxim goes, really the same albeit conceptually different. The principle seems, at first blush, absurd. Did the scholastics literally mean that every being is good? Is that supposed to include a cancer, a malaria parasite, an earthquake that kills millions? If every being is good, then no being is bad—but how can that be? To the contemporary philosophical mind, such bafflement is understandable. It derives from the systematic dismantling of the great scholastic edifice that took place over half a millennium. With the loss of the basic concepts out of which that edifice was built, the space created by those concepts faded out of existence as well. The convertibility principle, like virtually all the other scholastic principles (not all, since some do survive and thrive in analytic philosophy), could not persist in a post-scholastic space wholly alien to it.

Parametric VaR with goodness-of-fit tests based on EDF statistics for extreme returns

Parametric VaR (Value-at-Risk) is widely used due to its simplicity and easy calculation. However, the normality assumption, often used in the estimation of the parametric VaR, does not provide satisfactory estimates for risk exposure. Therefore, this study suggests a method for computing the parametric VaR based on goodness-of-fit tests using the empirical distribution function (EDF) for extreme returns, and compares the feasibility of this method for the banking sector in an emerging market and in a developed one. The paper also discusses possible theoretical contributions in related fields like enterprise risk management (ERM). © 2013 Elsevier Ltd.

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.