Nonparametric Tail Copula Estimation: An Application to Stock and Volatility Index Returns

In this study, we measure asymmetric negative tail dependence and discuss their statistical properties. In a simulation study, we show the reliability of nonparametric estimators of tail copula to measure not only the common positive lower and upper tail dependence, but also the negative “lower–upper” and “upper–lower” tail dependence. The use of this new framework is illustrated in an application to financial data. We detect the existence of asymmetric negative tail dependence between stock and volatility indices. Many common parametric copula models used in finance fail to capture this characteristic.     

A note on predictive inference for multivariate elliptically contoured distributions

The prediction problem is considered for the multivariate regression model with an elliptically contoured error distribution. We show that the predictive distribution under elliptical errors assumption is the same as that obtained under normally distributed error in both the Bayesian approach using an im-proper prior and the classical approach. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.     

Calibration Intervals in Linear Regression Models

Many of the existing methods of finding calibration intervals in simple linear regression rely on the inversion of prediction limits. In this article, we propose an alternative procedure which involves two stages. In the first stage, we find a confidence interval for the value of the explanatory variable which corresponds to the given future value of the response. In the second stage, we enlarge the confidence interval found in the first stage to form a confidence interval called, calibration interval, for the value of the explanatory variable which corresponds to the theoretical mean value of the future observation. In finding the confidence interval in the first stage, we have used the method based on hypothesis testing and percentile bootstrap. When the errors are normally distributed, the coverage probability of resulting calibration interval based on hypothesis testing is comparable to that of the classical calibration interval. In the case of non normal errors, the coverage probability of the calibration interval based on hypothesis testing is much closer to the target value than that of the calibration interval based on percentile bootstrap.     

On marginal likelihood inference for the intra-class correlation coefficient

A p-component set of responses have been constructed by a location-scale transformation to a p-component set of error variables, the covariance matrix of the set of error variables being of intra-class covariance structure:all variances being unity, and covariance being equal [IML0001]. A sample of size n has been described as a conditional structural model, conditional on the value of the intra-class correlation coefficient ρ. The conditional technique of structural inference provides the marginal likelihood function of ρ based on the standardized residuals. For the normal case, the marginal likelihood function of ρ is seen to be dependent on the standardized residuals through the sample intra-class correlation coefficient. By the likelihood modulation technique, the nonnull distribution of the sample intra-class correlation coefficient has also been obtained.     

The impact of a preliminary test for interaction in a 2 × 2 factorial trial

Preliminary tests of significance on the crucial assumptions are often done before drawing inferences of primary interest. In a factorial trial, the data may be pooled across the columns or rows for making inferences concerning the efficacy of the drugs {simple effect) in the absence of interaction. Pooling the data has an advantage of higher power due to larger sample size. On the other hand, in the presence of interaction, such pooling may seriously inflate the type I error rate in testing for the simple effect.

A preliminary test for interaction is therefore in order. If this preliminary test is not significant at some prespecified level of significance, then pool the data for testing the efficacy of the drugs at a specified α level. Otherwise, use of the corresponding cell means for testing the efficacy of the drugs at the specified α is recommended. This paper demonstrates that this adaptive procedure may seriously inflate the overall type I error rate. Such inflation happens even in the absence of interaction.

One interesting result is that the type I error rate of the adaptive procedure depends on the interaction and the square root of the sample size only through their product. One consequence of this result is as follows. No matter how small the non-zero interaction might be, the inflation of the type I error rate of the always-pool procedure will eventually become unacceptable as the sample size increases. Therefore, in a very large study, even though the interaction is suspected to be very small but non-zero, the always-pool procedure may seriously inflate the type I error rate in testing for the simple effects.

It is concluded that the 2 × 2 factorial design is not an efficient design for detecting simple effects, unless the interaction is negligible.     

A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.     

Impacts of financial crisis on social engagement in Hong Kong

While a financial crisis must afflict people financially, its impacts on people's social life are unclear. Essentially, different theories expect different impacts of the financial crisis on people's social engagement. The present study thereby clarifies the effect by examining the experienced impact of the crisis on social engagement, in terms of participation in voluntary association and caring for acquaintances. Data for the study came from a survey of 1170 Hong Kong Chinese adults. Results show that the experienced impact tended to raise the participation, which in turn appeared to encourage the caring. These results support the functional explanation, which holds that the fiscal crisis generates a need for functions of voluntary associations. Meanwhile, the results are at odds with the resource thesis, which expects that the crisis would deprive resources required for social engagement. The results imply that the financial crisis can be a lever to strengthen social engagement.     

Hypothesis testing via a penalized-likelihood approach

It is illustrated in this paper that hypothesis testing procedures can be derived based on the penalized likelihood approach. Based on this point of view, many traditional hypothesis tests, including the two-sample mean test, score test, and Hotelling’s $T^2$ test are revisited under the penalized likelihood framework. Similar framework is also applicable to the empirical likelihood.     

A Concept Mapping Study on Social Inclusion in Hong Kong

A focus group study involving concept mapping was conducted in September 2012 to investigate how the concept of social inclusion was understood by Hong Kong residents. It was a replication of an earlier UK study. Seven groups involving 61 participants (38 females; 23 males) were interviewed, including non-professional workers at a Non-government Organisation service, senior centre users, a mixed group of community residents, people with severe mental illness, professional social service providers, communication studies students, and social work students. Data analysis using Nvivo 10 and systematic thematic analysis identified six major themes including: (1) material resources and wealth, (2) work, (3) social (dis)harmony and diversity, (4) discrimination, (5) communication, and (6) participation in activities. An overall final model of Social Inclusion for Hong Kong based on concept maps for all seven groups is presented. The results will inform the conceptualisation and development of a Chinese-language measure of social inclusion (SCOPE-C) based on translation and cultural adaption of the Social and Community Opportunities Profile (SCOPE) developed in UK.     

A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis

In this paper we provide a formal yet simple and straightforward proof of the asymptotic χ² distribution for Cochran test statistic. Then, we show that the general form of this type of test statistics is invariant for the choice of weights. This fact is important since in practice many such test statistics are constructed with more complicated forms which usually require calculating generalized inverse matrices. Based on our results, we can simplify the construction of the test statistics. More importantly, properties such as anti-conservativeness of this type of test statistics can be drawn from Cochran test statistic. Furthermore, one can improve the performance of the tests by using some modified statistics with correction for small sample size situations.