Extended table of percentage points of the chi-square distribution /

"NAVWEPS report 7770. NOTS TP 2749."

Modified CADF and CIPS panel unit root statistics with standard chi-squared and normal limiting distributions

In an influential paper Pesaran ('A simple panel unit root test in presence of cross-section dependence', Journal of Applied Econometrics, Vol. 22, pp. 265-312, 2007) proposes two unit root tests for panels with a common factor structure. These are the CADF and CIPS test statistics, which are amongst the most popular test statistics in the literature. One feature of these statistics is that their limiting distributions are highly non-standard, making for relatively complicated implementation. In this paper, we take this feature as our starting point to develop modified CADF and CIPS test statistics that support standard chi-squared and normal inference.

Exercise sheet 9

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Exercise sheet 9 pdf

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Exercise sheet 4 pdf

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Exercise sheet 4

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Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.

Implementing aspects of Blueprint 2000: Investigating readiness expectations in selected elementary schools in Broward County, Florida

The purpose of this research study was to investigate if the determination of school readiness as it was evaluated by Broward County kindergarten teachers on the Florida's Expectations of School Readiness checklist can be attributed to the effects of gender, chronological age on school entry, racial or ethnic background, attending public preschool, native language other than English, or socioeconomic status.^ This is a descriptive study in which the number of expectations passed or failed for each of the identifier categories was compared. The Chi-squared distribution was used to evaluate the null hypothesis that "chronological age at entry to school, gender, race or ethnicity, native language other than English, public preschool experience, and socioeconomic status have no effect on the determination of readiness for school". Results were confirmed using t-tests, ANOVA, and linear regression models. The cohort of 1555 Broward County students in the study were evaluated using the Florida's Expectations for School Readiness checklist and were determined not ready for school during the initial data collection year 1996-1997.^ The determination of school readiness was significantly dependent on the gender, and racial or ethnic background of the students in the cohort. The socioeconomic status and native language other than English designations were significant for students only in the areas of preacademic, academic and literacy development. Chronological age on entry to school or attendance in public preschool prior to entry in kindergarten for the cohort was not significant in the determination of readiness for school.^ Given the fact that this study followed only students that were determined not ready for school, it is recommended that a second cohort of both "ready" and "not ready" students be studied. ^

Response probability distribution of built-up vibro-acoustic systems

The vibro-acoustic response of built-up structures, consisting of stiff components with low modal density and flexible components with high modal density, is sensitive to small imperfections in the flexible components. In this paper, the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, i.e., carrying a diffuse wave field, and by subsequently computing the response probability density function. The master system's mean squared response amplitude follows a singular noncentral complex Wishart distribution conditional on the subsystem energies. For a single degree of freedom, this is equivalent to a chi-square or an exponential distribution, depending on the loading conditions. The subsystem energies follow approximately a chi-square distribution when their relative variance is smaller than unity. The results are validated by application to plate structures, and good agreement with Monte Carlo simulations is found. © 2012 Acoustical Society of America.

Re-evaluation of pulmonary titanium dioxide nanoparticle distribution using the "relative deposition index": Evidence for clearance through microvasculature

ABSTRACT: BACKGROUND: Translocation of nanoparticles (NP) from the pulmonary airways into other pulmonary compartments or the systemic circulation is controversially discussed in the literature. In a previous study it was shown that titanium dioxide (TiO2) NP were "distributed in four lung compartments (air-filled spaces, epithelium/endothelium, connective tissue, capillary lumen) in correlation with compartment size". It was concluded that particles can move freely between these tissue compartments. To analyze whether the distribution of TiO2 NP in the lungs is really random or shows a preferential targeting we applied a newly developed method for comparing NP distributions. METHODS: Rat lungs exposed to an aerosol containing TiO2 NP were prepared for light and electron microscopy at 1 h and at 24 h after exposure. Numbers of TiO2 NP associated with each compartment were counted using energy filtering transmission electron microscopy. Compartment size was estimated by unbiased stereology from systematically sampled light micrographs. Numbers of particles were related to compartment size using a relative deposition index and chi-squared analysis. RESULTS: Nanoparticle distribution within the four compartments was not random at 1 h or at 24 h after exposure. At 1 h the connective tissue was the preferential target of the particles. At 24 h the NP were preferentially located in the capillary lumen. CONCLUSION: We conclude that TiO2 NP do not move freely between pulmonary tissue compartments, although they can pass from one compartment to another with relative ease. The residence time of NP in each tissue compartment of the respiratory system depends on the compartment and the time after exposure. It is suggested that a small fraction of TiO2 NP are rapidly transported from the airway lumen to the connective tissue and subsequently released into the systemic circulation.

Analysis of distrubances in large interconnected power systems

World economies increasingly demand reliable and economical power supply and distribution. To achieve this aim the majority of power systems are becoming interconnected, with several power utilities supplying the one large network. One problem that occurs in a large interconnected power system is the regular occurrence of system disturbances which can result in the creation of intra-area oscillating modes. These modes can be regarded as the transient responses of the power system to excitation, which are generally characterised as decaying sinusoids. For a power system operating ideally these transient responses would ideally would have a “ring-down” time of 10-15 seconds. Sometimes equipment failures disturb the ideal operation of power systems and oscillating modes with ring-down times greater than 15 seconds arise. The larger settling times associated with such “poorly damped” modes cause substantial power flows between generation nodes, resulting in significant physical stresses on the power distribution system. If these modes are not just poorly damped but “negatively damped”, catastrophic failures of the system can occur. To ensure system stability and security of large power systems, the potentially dangerous oscillating modes generated from disturbances (such as equipment failure) must be quickly identified. The power utility must then apply appropriate damping control strategies. In power system monitoring there exist two facets of critical interest. The first is the estimation of modal parameters for a power system in normal, stable, operation. The second is the rapid detection of any substantial changes to this normal, stable operation (because of equipment breakdown for example). Most work to date has concentrated on the first of these two facets, i.e. on modal parameter estimation. Numerous modal parameter estimation techniques have been proposed and implemented, but all have limitations [1-13]. One of the key limitations of all existing parameter estimation methods is the fact that they require very long data records to provide accurate parameter estimates. This is a particularly significant problem after a sudden detrimental change in damping. One simply cannot afford to wait long enough to collect the large amounts of data required for existing parameter estimators. Motivated by this gap in the current body of knowledge and practice, the research reported in this thesis focuses heavily on rapid detection of changes (i.e. on the second facet mentioned above). This thesis reports on a number of new algorithms which can rapidly flag whether or not there has been a detrimental change to a stable operating system. It will be seen that the new algorithms enable sudden modal changes to be detected within quite short time frames (typically about 1 minute), using data from power systems in normal operation. The new methods reported in this thesis are summarised below. The Energy Based Detector (EBD): The rationale for this method is that the modal disturbance energy is greater for lightly damped modes than it is for heavily damped modes (because the latter decay more rapidly). Sudden changes in modal energy, then, imply sudden changes in modal damping. Because the method relies on data from power systems in normal operation, the modal disturbances are random. Accordingly, the disturbance energy is modelled as a random process (with the parameters of the model being determined from the power system under consideration). A threshold is then set based on the statistical model. The energy method is very simple to implement and is computationally efficient. It is, however, only able to determine whether or not a sudden modal deterioration has occurred; it cannot identify which mode has deteriorated. For this reason the method is particularly well suited to smaller interconnected power systems that involve only a single mode. Optimal Individual Mode Detector (OIMD): As discussed in the previous paragraph, the energy detector can only determine whether or not a change has occurred; it cannot flag which mode is responsible for the deterioration. The OIMD seeks to address this shortcoming. It uses optimal detection theory to test for sudden changes in individual modes. In practice, one can have an OIMD operating for all modes within a system, so that changes in any of the modes can be detected. Like the energy detector, the OIMD is based on a statistical model and a subsequently derived threshold test. The Kalman Innovation Detector (KID): This detector is an alternative to the OIMD. Unlike the OIMD, however, it does not explicitly monitor individual modes. Rather it relies on a key property of a Kalman filter, namely that the Kalman innovation (the difference between the estimated and observed outputs) is white as long as the Kalman filter model is valid. A Kalman filter model is set to represent a particular power system. If some event in the power system (such as equipment failure) causes a sudden change to the power system, the Kalman model will no longer be valid and the innovation will no longer be white. Furthermore, if there is a detrimental system change, the innovation spectrum will display strong peaks in the spectrum at frequency locations associated with changes. Hence the innovation spectrum can be monitored to both set-off an “alarm” when a change occurs and to identify which modal frequency has given rise to the change. The threshold for alarming is based on the simple Chi-Squared PDF for a normalised white noise spectrum [14, 15]. While the method can identify the mode which has deteriorated, it does not necessarily indicate whether there has been a frequency or damping change. The PPM discussed next can monitor frequency changes and so can provide some discrimination in this regard. The Polynomial Phase Method (PPM): In [16] the cubic phase (CP) function was introduced as a tool for revealing frequency related spectral changes. This thesis extends the cubic phase function to a generalised class of polynomial phase functions which can reveal frequency related spectral changes in power systems. A statistical analysis of the technique is performed. When applied to power system analysis, the PPM can provide knowledge of sudden shifts in frequency through both the new frequency estimate and the polynomial phase coefficient information. This knowledge can be then cross-referenced with other detection methods to provide improved detection benchmarks.

Association analysis of a highly polymorphic CAG Repeat in the human potassium channel gene KCNN3 and migraine susceptibility

Background Migraine is a polygenic multifactorial disease, possessing environmental and genetic causative factors with multiple involved genes. Mutations in various ion channel genes are responsible for a number of neurological disorders. KCNN3 is a neuronal small conductance calcium-activated potassium channel gene that contains two polyglutamine tracts, encoded by polymorphic CAG repeats in the gene. This gene plays a critical role in determining the firing pattern of neurons and acts to regulate intracellular calcium channels. Methods The present association study tested whether length variations in the second (more 3') polymorphic CAG repeat in exon 1 of the KCNN3 gene, are involved in susceptibility to migraine with and without aura (MA and MO). In total 423 DNA samples from unrelated individuals, of which 202 consisted of migraine patients and 221 non-migraine controls, were genotyped and analysed using a fluorescence labelled primer set on an ABI310 Genetic Analyzer. Allele frequencies were calculated from observed genotype counts for the KCNN3 polymorphism. Analysis was performed using standard contingency table analysis, incorporating the chi-squared test of independence and CLUMP analysis. Results Overall, there was no convincing evidence that KCNN3 CAG lengths differ between Caucasian migraineurs and controls, with no significant difference in the allelic length distribution of CAG repeats between the population groups (P = 0.090). Also the MA and MO subtypes did not differ significantly between control allelic distributions (P > 0.05). The prevalence of the long CAG repeat (>19 repeats) did not reach statistical significance in migraineurs (P = 0.15), nor was there a significant difference between the MA and MO subgroups observed compared to controls (P = 0.46 and P = 0.09, respectively), or between MA vs MO (P = 0.40). Conclusion This association study provides no evidence that length variations of the second polyglutamine array in the N-terminus of the KCNN3 channel exert an effect in the pathogenesis of migraine.

Investigation of a neuronal nitric oxide synthase gene (NOS1) polymorphism in a multiple sclerosis population

Multiple Sclerosis (MS) is a chronic neurological disease characterized by demyelination associated with infiltrating white blood cells in the central nervous system (CNS). Nitric oxide synthases (NOS) are a family of enzymes that control the production of nitric oxide. It is possible that neuronal NOS could be involved in MS pathophysiology and hence the nNOS gene is a potential candidate for involvement in disease susceptibility. The aim of this study was to determine whether allelic variation at the nNOS gene locus is associated with MS in an Australian cohort. DNA samples obtained from a Caucasian Australian population affected with MS and an unaffected control population, matched for gender, age and ethnicity, were genotyped for a microsatellite polymorphism in the promoter region of the nNOS gene. Allele frequencies were compared using chi-squared based statistical analyses with significance tested by Monte Carlo simulation. Allelic analysis of MS cases and controls produced a chi-squared value of 5.63 with simulated P = 0.96 (OR(max) = 1.41, 95% CI: 0.926-2.15). Similarly, a Mann-Whitney U analysis gave a non-significant P-value of 0.377 for allele distribution. No differences in allele frequencies were observed for gender or clinical course subtype (P > 0.05). Statistical analysis indicated that there is no association of this nNOS variant and MS and hence the gene does not appear to play a genetically significant role in disease susceptibility.