The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Test for Independence of the Variables with Missing Elements in One and the Same Column of the Empirical Correlation Matrix

2000 Mathematics Subject Classification: 62H15, 62H12.

Il problema della Nearest Correlation Matrix: il metodo delle proiezioni alternate e l'accelerazione di Anderson

Un problema frequente nell'analisi dei dati del mondo reale è quello di lavorare con dati "non coerenti", poiché raccolti a tempi asincroni o a causa di una successiva modifica "manuale" per ragioni che esulano da quelle matematiche. In particolare l'indagine dell'elaborato nasce da motivazioni di tipo finanziario, dove strumenti semplici come le matrici di correlazione, che sono utilizzate per capire le relazioni tra vari titoli o strategie, non rispettano delle caratteristiche cruciali a causa dell'incoerenza dei dati. A partire da queste matrici "invalide" si cerca la matrice di correlazione più vicina in norma, in modo da mantenere più informazioni originali possibili. Caratterizzando la soluzione del problema tramite analisi convessa, si utilizza il metodo delle proiezioni alternate, largamente utilizzato per la sua flessibilità anche se penalizzato dalla velocità di convergenza lineare. Viene quindi proposto l'utilizzo dell'accelerazione di Anderson, una tecnica per accelerare la convergenza dei metodi di punto fisso che, applicata al metodo di proiezione alternata, porta significativi miglioramenti in termini di tempo computazionale e numero di iterazioni. Si mostra inoltre come, nel caso di varianti del problema, l'applicazione dell'accelerazione di Anderson abbia un effetto maggiore rispetto al caso del problema "classico".

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Modelling world investment markets using threshold conditional correlation models

In this paper we propose a parsimonious regime-switching approach to model the correlations between assets, the threshold conditional correlation (TCC) model. This method allows the dynamics of the correlations to change from one state (or regime) to another as a function of observable transition variables. Our model is similar in spirit to Silvennoinen and Teräsvirta (2009) and Pelletier (2006) but with the appealing feature that it does not suffer from the course of dimensionality. In particular, estimation of the parameters of the TCC involves a simple grid search procedure. In addition, it is easy to guarantee a positive definite correlation matrix because the TCC estimator is given by the sample correlation matrix, which is positive definite by construction. The methodology is illustrated by evaluating the behaviour of international equities, govenrment bonds and major exchange rates, first separately and then jointly. We also test and allow for different parts in the correlation matrix to be governed by different transition variables. For this, we estimate a multi-threshold TCC specification. Further, we evaluate the economic performance of the TCC model against a constant conditional correlation (CCC) estimator using a Diebold-Mariano type test. We conclude that threshold correlation modelling gives rise to a significant reduction in portfolio´s variance.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement -SCR-, under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.

Detection of protein fold similarity based on correlation of amino acid properties

An increasing number of proteins with weak sequence similarity have been found to assume similar three-dimensional fold and often have similar or related biochemical or biophysical functions. We propose a method for detecting the fold similarity between two proteins with low sequence similarity based on their amino acid properties alone. The method, the proximity correlation matrix (PCM) method, is built on the observation that the physical properties of neighboring amino acid residues in sequence at structurally equivalent positions of two proteins of similar fold are often correlated even when amino acid sequences are different. The hydrophobicity is shown to be the most strongly correlated property for all protein fold classes. The PCM method was tested on 420 proteins belonging to 64 different known folds, each having at least three proteins with little sequence similarity. The method was able to detect fold similarities for 40% of the 420 sequences. Compared with sequence comparison and several fold-recognition methods, the method demonstrates good performance in detecting fold similarities among the proteins with low sequence identity. Applied to the complete genome of Methanococcus jannaschii, the method recognized the folds for 22 hypothetical proteins.

The beliefs of nurses who were involved in a whistleblowing event

Background. Nursing codes of ethics bind nurses to the role of patient advocate and compel them to take action when the rights or safety of a patient are jeopardized. Reporting misconduct is known as whistleblowing and studies indicate that there are personal and professional risks involved in blowing the whistle. Aim. The aim of this study was to explore the beliefs of nurses who wrestled with this ethical dilemma. Design. A descriptive survey design was used to examine the beliefs of nurses in Western Australia who reported misconduct (whistleblowers) and of those who did not report misconduct (nonwhistleblowers). Methods. The instrument listed statements from current ethical codes, statements from traditional views on nursing and statements of beliefs related to the participant's whistleblowing experience. Respondents were asked to rate each item on a five-point Likert format which ranged from strongly agree to strongly disagree. Data were analysed using a Pearson's correlation matrix and one-way ANOVA. To further explore the data, a factor analysis was run with varimax rotation. Results. Results indicated that whistleblowers supported the beliefs inherent in patient advocacy, while nonwhistleblowers retained a belief in the traditional role of nursing. Participants who reported misconduct (whistleblowers) supported the belief that nurses were primarily responsible to the patient and should protect a patient from incompetent or unethical people. Participants who did not report misconduct (nonwhistleblowers) supported the belief that nurses are obligated to follow a physician's order at all times and that nurses are equally responsible to the patient, the physician and the employer. Conclusion. These findings indicate that nurses may respond to ethical dilemmas based on different belief systems.

Does participation in a pain course based on the international association for the study of pain's curricula guidelines change student knowledge about pain?

The People in Pain course was set up as a joint initiative of the Departments of Occupational Therapy and Physiotherapy within the School of Health and Rehabilitation Sciences at The University of Queensland. It was instigated in response to the publication of Pain Curricula for Occupational Therapy and Physiotherapy by the International Association for the Study of Pain (IASP) in 1994 (1). The first year it was offered, the "People in Pain" course comprised 14 h of lecture content. It was then expanded to encompass 28 h of lectures and seminar involvement. OBJECTIVES: To evaluate the impact of participation in a university pain course that meets the IASP pain curricula guidelines to increase health professional students' knowledge about pain. METHODS: Students who participated in the People in Pain course over the first three years were invited to complete the Revised Pain Knowledge and Attitudes Questionnaire (R-PKAQ) pre- and postcourse. Data obtained from 22 students in the short course formed a pilot project, and data from 22 students in the longer version of the course were used in the present study. RESULTS: Examination of the correlation matrix indicated substantial correlations between all R-PKAQ subscales except physiological basis of pain and pharmacological management of pain. In both the pilot project during the first year of the course and the expanded course in the following two years, significant improvement was found in the students' knowledge on five of the six subscales of the R-PKAQ: physiological basis of pain, psychological factors of pain perception, assessment and measurement of pain, cognitive-behavioural methods of pain relief, and pharmacological management of pain. Improvements in the developmental aspects of pain perception subscale failed to reach significance. CONCLUSIONS: An integrated pain course developed according to the pain curriculum guidelines developed by the IASP resulted in increased student knowledge regardless of the length of the program attended.