Ping-Hung Hsieh

Robustness of Tail Index Estimation

Abstract The implementation of the Hill estimator, which estimates the heaviness of the tail of a distribution, requires a choice of the number of extreme observations in the tails, r from a sample of size n where 2 ≤ r + 1 ≤ n. This article is concerned with a robust procedure of choosing an optimal r. Thus, an estimation procedure, δ s , based on the idea of spacing statistics, H(r) is developed. The proposed decision rule for choosing r under the squared error loss is found to be a simple function of the sample size. The proposed rule is then illustrated across a wide range of data, including insurance claims, currency exchange rate returns, and city size.

Decision support for unrelated parallel machine scheduling with discrete controllable processing times

A scheduling problem involving discrete controllable processing times is considered.The objectives are to minimize some scheduling criteria.We develop polynomial time algorithms for the considered problems.We further consider the NP-hard problem of the makespan case.An integer programming and a heuristic are presented to solve the NP-hard problem. In a manufacturing or service system, the actual processing time of a job can be controlled by the amount of an indivisible resource allocated, such as workers or auxiliary facilities. In this paper, we consider unrelated parallel-machine scheduling problems with discrete controllable processing times. The processing time of a job is discretely controllable by the allocation of indivisible resources. The planner must make decisions on whether or how to allocate resources to jobs during the scheduling horizon to optimize the performance measures. The objective is to minimize the total cost including the cost measured by a standard criterion and the total processing cost. We first consider three scheduling criterions: the total completion time, the total machine load, and the total earliness and tardiness penalties. If the number of machines and the number of possible processing times are fixed, we develop polynomial time algorithms for the considered problems. We then consider the minimization problem of the makespan cost plus the total processing cost and present an integer programming method and a heuristic method to solve the studied problem.

Tales from the tail: Robust estimation of moments of environmental data with one-sided detection limits

Estimating the means and standard deviations of environmental data remains a great challenge because a substantial percentage of observations lies below or above detection limits. The inadequacy of several common, ad hoc estimation procedures is clear; this study instead proposes a robust moment estimation procedure for environmental data with a one-sided detection limit. The procedure assumes that the tails of the underlying distribution of the (transformed) data are symmetric, and censoring only occurs on one side. Through an application of the Renyi representation theorem, it is possible to use observations from the other side to learn the shape of the distribution below the detection limit, without specifying any particular parametric model, and consequently, derive the moment estimates of the distribution. A simulation provides a comparison of estimation performance between the proposed procedure and several existing estimators, and several real-life samples offer a good illustration.

An exploratory first step in teletraffic data modeling: evaluation of long-run performance of parameter estimators

Examination of the tail behavior of a distribution F that generates teletraffic measurements is an important first step toward building a network model that explains the link between heavy tails and long-range dependence exhibited in such data. When knowledge of the tail behavior of F is vague, the family of the generalized Pareto distributions (GPDs) can be used to approximate the tail probability of F, and the value of its shape parameter characterizes the tail behavior. To detect tail behavior of F between two host computers on a network, the estimation procedure must be carried out over all possible combinations of host computers, and thus, the performance of the estimator under repeated use becomes the primary concern. In this article, we evaluate the long-run performance of several existing estimation procedures and propose a Bayes estimator to overcome some of the shortcomings. The conditions in which the procedures perform well in the long run are reported, and a simple rule of thumb for choosing an appropriate estimator for the task of repeated estimation is recommended.

Process Control for the Vector Autoregressive Model

Multivariate monitoring techniques for serially correlated observations have been widely used in various applications. This study examines several issues that have arisen in relation to the statistical quality control for the vector autoregressive (VAR) model, using a Monte Carlo approach. Different versions of the Hotelling T2 statistic and control limits to monitor the VAR-type process for both Phase I and Phase II schemes can be specified for different sample sizes and configurations of the model. Our simulation study suggests that the Hotellings T2 statistic can be tested against the χ2 critical values during Phase I, but should be tested against scaled F critical values during Phase II. An unbiased covariance estimate of residuals is also recommended during Phase II when sample size is typically small. By reanalyzing some real data examples, the authors offer new conclusions. Copyright

On the Hotelling T 2 control chart for the vector autoregressive process

A vector autoregressive (VAR) model has become a popular multivariate monitoring technique for serially correlated observations often observed in practice. In this article, we examine, via a Monte Carlo approach, the effect of a shift in the model parameter and the sample size in both Phase I and Phase II schemes on control chart statistics, namely, different versions of Hotellings T2 when a VAR model is employed. The effects are reported and specific T 2 statistics under various sample sizes is recommended.

ON BAYESIAN PREDICTIVE MOMENTS OF NEXT RECORD VALUE USING THREE-PARAMETER GAMMA PRIORS

A forecasting model of next record value proposed by Hill [1] assumes the underlying distribution F(x) is of an algebraic functional form with a shape parameter α for large x. That is, 1 − F(x) ≃Cx −α, for large x. In this article, we extend his model by incorporating a three-parameter Gamma prior of α to derive analytical solutions of the predictive distribution and moments of X given that X is a new record value. These closed-form formulas can be represented as ratios of moments of Gamma distributions. We apply the proposed model to a real-life data set that consists of the insured property losses of 33 catastrophes caused by tropical storms in the United States in 1995. The example illustrates the importance of incorporating prior experience and accounting for uncertainty in parameter estimation when forecasting record values. Both considerations are the main ingredients in the development of the proposed model.

Map- or list-based recommender agents? Does the map metaphor fulfill its promise?:

We present a spatialization of digital library content based on item similarity and an experiment which compares the performance of this spatialization relative to a simple list-based display. Items in the library are elementary school, middle school, and high school science and engineering learning resources. Spatialization and visualization are accomplished through two-dimensional interactive Sammon mapping of pairwise item similarities computed from the joint occurrence of word bigrams. The 65 science teachers participating in the experiment were asked to search the library for curricular items they would consider using as part of one or more teaching assignments. The results indicate that whereas the spatializations adequately capture the salient features of the library’s content and teachers actively use them, item retrieval rates, task-completion time, and perceived utility do not significantly differ from the semantically poorer but easier to comprehend and navigate list-based representations. These results put into question the usefulness of the rapidly increasing supply of information spatializations.