New recursive estimators of the time-average variance constant

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with \(O(1)\) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with \(O(1)\) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the \(O(1)\) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is \(2^{10/3}3^{-2} \fallingdotseq 1.12\) times that of the optimal off-line TAVC estimator.     

A search of maximum generalized resolution quaternary-code designs via integer linear programming

Quaternary-code (QC) designs, an attractive class of nonregular fractional factorial designs, have received much attention due to their theoretical elegance and practical applicability. Some recent works of QC designs revealed their good properties over their regular counterparts under commonly used criteria. We develop an optimization tool that can maximize the generalized resolution of a QC design of a given size. The problem can be recast as an integer linear programming (ILP) problem through a linear simplification that combines the \(k\)- and \(a\)-equations, even though the generalized resolution does not linearly depend on the aliasing indexes. The ILP surprisingly improves a class of \((1/16)\)th-fraction QC designs with higher generalized resolutions. It also applies to obtain some \((1/64)\)th-fraction QC designs with maximum generalized resolutions, and these QC designs generally have higher generalized resolutions than the regular designs of the same size.     

澳门旅游博彩形象的实证研究

澳门博彩业回归后迅速发展,随著"澳门历史城区"被列入"世界文化遗产",该行业更出现前所未有的繁荣景象。然而,除了"赌城"的形象外,澳门的旅游博彩形象还有甚么元素呢?本文结合了"结构法"与"非结构法",针对澳门旅游博彩形象进行问卷调查,来了解它的内涵及意义,并尝试提出一些适合澳门旅游博彩形象发展的建议,以利澳门这个"龙头"产业的可持续发展。     

The Escalator: A Conveyor of Hong Kong's Culture

People believe that escalators provide a moreattractive, convenient, and physically less-demandingpedestrian access from one place to another. However, itdoes not mean all of us have to like them. Escalators do not only affect our perception of speed, butthe most important concern is that this urban objectalso influences our social relationships and humancommunication. Under the transmission of this urban object, we are treated as components (a what),rather than human beings (a who). Thus, this articlediscusses how modernist thinking affects how we see thisobject and ourselves, and examines the relative worth of it, in relation to the social lossincurred in the present or future. This article alsodiscusses how its presence in many of the daily settingsof urban life affects the culture, meaning and quality of life.Requests for reprints should be addressed SIU Kin Wai Michael, School of Design, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong.     

Sample Size and Power Calculation in Comparing Diagnostic Accuracy of Biomarkers with Pooled Assessments

When testing of a biomarker is costly, pooling of samples becomes a useful and efficient alternative (Faraggi et al., 2003). In this paper, we develop procedures for sample size and power calculations for planning a study comparing the accuracy of biomarkers in diagnosis of diseases with pooled samples. Explicit formulas are derived for several important pooling strategies. The effects of pooling samples on sample size and power of the test are also discussed.     

Butterfly diversity,habitat and vegetation usage in Hong Kong urban parks

The conservation value of urban parks for butterfly communities remains poorly understood, particularly for tropical butterflies in Asia. We conducted point count and route transect butterfly surveys, and used them to sample four habitats located within 13 urban parks across Hong Kong. We found 1054 individuals and 58 species of butterflies recorded in 60 survey hours over 6 months. This represents approximately one quarter of the entire known Hong Kong butterfly species list. Over 30 % of the individuals counted were Catospilia sp. but six of the species identified are classified locally as rare or very rare. Tree-covered habitats and grasslands showed higher butterfly diversity than open areas. The most common butterfly behavior was “directed flight,” which we also found to be habitat-dependent and most common in ponds and open areas. We additionally observed the use of vegetation in urban parks, which included 40 species of nectar plant and four records of butterfly oviposition. The high butterfly diversity, presence of rare species and usage of vegetation (especially as a nectar resource) we documented in this study suggests that urban parks have some conservation value for Hong Kong. However, the use of pesticides and heavy vegetation clearing may limit significant butterfly reproduction and population growth. Altogether these results emphasize the diversity of uses of urban parks for butterflies in Hong Kong while also providing possible directions for improvement in habitat and vegetation management that could increase urban park value for biodiversity.     

High‐order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth

Estimation of time‐average variance constant (TAVC), which is the asymptotic variance of the sample mean of a dependent process, is of fundamental importance in various fields of statistics. For frequentists, it is crucial for constructing confidence interval of mean and serving as a normalizing constant in various test statistics and so forth. For Bayesians, it is widely used for evaluating effective sample size and conducting convergence diagnosis in Markov chain Monte Carlo method. In this paper, by considering high‐order corrections to the asymptotic biases, we develop a new class of TAVC estimators that enjoys optimal ‐convergence rates under different degrees of the serial dependence of stochastic processes. The high‐order correction procedure is applicable to estimation of the so‐called smoothness parameter, which is essential in determining the optimal bandwidth. Comparisons with existing TAVC estimators are comprehensively investigated. In particular, the proposed optimal high‐order corrected estimator has the best performance in terms of mean squared error.     

Bayesian covariance matrix estimation using a mixture of decomposable graphical models

We present a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs in more efficiently estimating the covariance matrix. The prior requires knowing the number of decomposable graphs for each graph size and we give a simulation method for estimating these counts. We also present a Markov chain Monte Carlo method for estimating the posterior distribution of the covariance matrix that is much more efficient than current methods. Both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.