Simulation-Based Finite-Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.

Testing Normality : A GMM Approach

In this paper, we consider testing marginal normal distributional assumptions. More precisely, we propose tests based on moment conditions implied by normality. These moment conditions are known as the Stein (1972) equations. They coincide with the first class of moment conditions derived by Hansen and Scheinkman (1995) when the random variable of interest is a scalar diffusion. Among other examples, Stein equation implies that the mean of Hermite polynomials is zero. The GMM approach we adopted is well suited for two reasons. It allows us to study in detail the parameter uncertainty problem, i.e., when the tests depend on unknown parameters that have to be estimated. In particular, we characterize the moment conditions that are robust against parameter uncertainty and show that Hermite polynomials are special examples. This is the main contribution of the paper. The second reason for using GMM is that our tests are also valid for time series. In this case, we adopt a Heteroskedastic-Autocorrelation-Consistent approach to estimate the weighting matrix when the dependence of the data is unspecified. We also make a theoretical comparison of our tests with Jarque and Bera (1980) and OPG regression tests of Davidson and MacKinnon (1993). Finite sample properties of our tests are derived through a comprehensive Monte Carlo study. Finally, three applications to GARCH and realized volatility models are presented.

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.

Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

Ballet-performing normality in the face of crisis

This paper contextualises the framework and methodology for producing the video performance Ballet, by Szuper Gallery (Susanne Clausen & Pavlo Kerestey), which was initiated through an encounter with an archive of rural information and propaganda films from the Museum of English Rural Life [MERL] in Reading, UK. This project looked at ways of extrapolating filmed gestures from the MERL films to choreograph a large-scale performance film and to consider how this practice-led research could instigate a new way of engaging with and interpreting the MERL film collection. The resulting video was produced in 2009 and was first exhibited at MERL, where it became part of the archive. This was followed by a series of international screenings. I will set out the surrounding research in and around the archive propaganda films, focusing on the performances by rural extras (background actors) in these films, while looking at the way one could understand the relation between a future-past, or tradition and accident in these films (Massumi, 1993). I will pair this with a reflection on the cultural reading of the extras (Didi-Huberman, 2009) and the notion of social choreography (Hewitt, 2005) in this context. I will then lay out reflections on artistic methods for the final performance, a Crash Choreography, based on calculated, but spontaneous encounters.

Normality mining: privacy implications of behavioral profiles drawn from GPS enabled mobile phones

There is growing interest in the ways in which the location of a person can be utilized by new applications and services. Recent advances in mobile technologies have meant that the technical capability to record and transmit location data for processing is appearing in off-the-shelf handsets. This opens possibilities to profile people based on the places they visit, people they associate with, or other aspects of their complex routines determined through persistent tracking. It is possible that services offering customized information based on the results of such behavioral profiling could become commonplace. However, it may not be immediately apparent to the user that a wealth of information about them, potentially unrelated to the service, can be revealed. Further issues occur if the user agreed, while subscribing to the service, for data to be passed to third parties where it may be used to their detriment. Here, we report in detail on a short case study tracking four people, in three European member states, persistently for six weeks using mobile handsets. The GPS locations of these people have been mined to reveal places of interest and to create simple profiles. The information drawn from the profiling activity ranges from intuitive through special cases to insightful. In this paper, these results and further extensions to the technology are considered in light of European legislation to assess the privacy implications of this emerging technology.

“Normality is threatened by the Monster”: Robin Wood, Romero and zombies

A tribute to Robin Wood, focusing on his influence on horror criticism, and more specifically, on his appraisal of George A. Romero as ‘a great and audacious filmmaker’ through detailed consideration of his zombie movies. The article considers the key elements of his extraordinary influence on horror criticism, and a detailed examination of the monster which most directly responds to horror’s potential ambivalence: the zombie. In order to consider the ambivalence in the relationship between normality and the monster – that central and most important component of Wood’s horror criticism – created by Romero’s zombies, analysis focuses on the materiality of the films through close attention to the bodies on-screen.

Normality under uncertainty

Consider the demand for a good whose consumption be chosen prior to the resolution of uncertainty regarding income. How do changes in the distribution of income affect the demand for this good? In this paper we show that normality, is sufficient to guarantee that consumption increases of the Radon-Nikodym derivative of the new distribution with respect to the old is non-decreasing in the whole domain. However, if only first order stochastic dominance is assumed more structure must be imposed on preferences to guanantee the validity of the result. Finally a converse of the first result also obtains. If the change in measure is characterized by non-decreasing Radon-Nicodyn derivative, consumption of such a good will always increase if and only if the good is normal.

Second-growth western white pine stands : site index and species changes, normality percentage trends, mortality /

Includes bibliographical references (p. 58-60).

Breaking down the non-normality of daily stock returns

This paper investigates whether the non-normality typically observed in daily stock-market returns could arise because of the joint existence of breaks and GARCH effects. It proposes a data-driven procedure to credibly identify the number and timing of breaks and applies it on the benchmark stock-market indices of 27 OECD countries. The findings suggest that a substantial element of the observed deviations from normality might indeed be due to the co-existence of breaks and GARCH effects. However, the presence of structural changes is found to be the primary reason for the non-normality and not the GARCH effects. Also, there is still some remaining excess kurtosis that is unlikely to be linked to the specification of the conditional volatility or the presence of breaks. Finally, an interesting sideline result implies that GARCH models have limited capacity in forecasting stock-market volatility.

Criterion of Normality of the Completely Regular Topology of Separate Continuity

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.