Heung Wong

Models for extremes using the extended three- parameter Burr XII system with application to flood frequency analysis

Abstract Abstract A new theoretically-based distribution in frequency analysis is proposed. The extended three-parameter Burr XII distribution includes the generalized Pareto distribution, which is used to model the exceedences over threshold; log-logistic distribution, which is also advocated in flood frequency analysis; and Weibull distribution, which is a part of the generalized extreme value distribution used to model annual maxima as special cases. The extended Burr distribution is flexible to approximate extreme value distribution. Note that both the generalized Pareto and generalized extreme value distributions are limiting results in modelling the exceedences over threshold and block extremes, respectively. From a modelling perspective, generalization might be necessary in order to obtain a better fit. The extended three-parameter Burr XII distribution is therefore a meaningful candidate distribution in the frequency analysis. Maximum likelihood estimation for this distribution is investigated in the paper. The use of the extended three-parameter Burr XII distribution is demonstrated using data from China.

Modelling and forecasting by wavelets, and the application to exchange rates

This paper investigates the modelling and forecasting method for non-stationary time series. Using wavelets, the authors propose a modelling procedure that decomposes the series as the sum of three separate components, namely trend, harmonic and irregular components. The estimates suggested in this paper are all consistent. This method has been used for the modelling of US dollar against DM exchange rate data, and ten steps ahead (2 weeks) forecasting are compared with several other methods. Under the Average Percentage of forecasting Error (APE) criterion, the wavelet approach is the best one. The results suggest that forecasting based on wavelets is a viable alternative to existing methods.

Varying-coefficient single-index model

In this paper, the varying-coefficient single-index model (VCSIM) is proposed. It can be seen as a generalization of the semivarying-coefficient model by changing its constant coefficient part to a nonparametric component, or a generalization of the partially linear single-index model by replacing the constant coefficients of its linear part with varying coefficients. Based on the local linear method, average method and backfitting technique, the estimates of the unknown parameters and the unknown functions of the VCSIM are obtained and their asymptotic distributions are derived. Both simulated and real data examples are given to illustrate the model and the proposed estimation methodology.

The value of combining forecasts in inventory management – a case study in banking

Managing inventories in the face of uncertain stochastic demand requires an investment in safety stocks. These are related to the accuracy in forecasting future demands and the noise in the demand generation process. Reducing the demand forecasting error can free up capital and space, and reduce the operating costs of managing the inventories. A leading bank in Hong Kong consumes more than three hundred kinds of printed forms for its daily operations. A major problem of its inventory control system for the forms management is to forecast the monthly demand of these forms. In this study the idea of combining forecasts is introduced and its practical application is addressed. The individual forecasts come from well established time series models and the weights for combination are estimated with Quadratic Programming. The combined forecast is found to perform better than any of the individual forecasts.

The Hybrid Fuzzy Least-Squares Regression Approach to Modeling Manufacturing Processes

Uncertainty in manufacturing processes is caused both by randomness, as in material properties, and by fuzziness, as in the inexact knowledge. Previous research has seldom considered these two types of uncertainty when modeling manufacturing processes. In this paper, a hybrid fuzzy least-squares regression (HFLSR) approach to modeling manufacturing processes, which does take into consideration these two types of uncertainty, is proposed and described, and a new form of weighted fuzzy arithmetic is introduced to develop the hybrid fuzzy least-squares regression method. The proposed HFLSR approach not only features the capability of dealing with the two types of uncertainty, but also addresses the consideration of replication of responses in experiments. To investigate the effectiveness of the proposed approach to process modeling, it was applied to the modeling solder paste dispensing process. Modeling results were compared with those based on statistical regression and fuzzy linear regression. It was found that the accuracy of prediction based on the HFLSR is slightly better than that based on statistical regression and much better than that based on the Peters fuzzy regression.

Estimation of nonlinear time series with conditional heteroscedastic variances by iteratively weighted least squares

Abstract In this paper we consider a unified approach for fitting conditionally nonlinear time series models with heteroscedastic variances. The model considered is completely general, requiring only that the forms of the mean and conditional variance functions be specified. Based on the recent results of Mak (1993) on general estimating equations, we derive a convenient expression for the conditional information matrix. Furthermore, it is shown that estimation in such models can be performed via an iteratively weighted least squares algorithm (IWLS), so that the computational problems involved can be conveniently handled by many popular statistical packages. Its implementation is numerically illustrated using the “threshold plus ARCH” model. The algorithm is also demonstrated using both simulated and real data to be superior to the popular BHHH algorithm, which requires a much longer computing time and fails to converge if initial values are not chosen properly.

Takagi-Sugeno neural fuzzy modeling approach to fluid dispensing for electronic packaging

In the semiconductor manufacturing industry fluid dispensing is a popular process which is commonly used in die-bonding as well as in microchip encapsulation for electronic packaging. Modeling the fluid dispensing process is important because it enables us to understand the process behavior, as well as determine the optimum operating conditions of the process for a high yield, low cost and robust operation. Previous studies of fluid dispensing mainly focus on the development of analytical models. However, an analytical model for fluid dispensing, which can provide accurate results, is very difficult to develop because of the complex behavior of fluid dispensing and high degree of uncertainty associated with the process in a real world environment. In this project, Takagi-Sugeno neural fuzzy systems, is introduced to model the fluid dispensing process for microchip encapsulation. Two process models were generated for the two quality characteristics; encapsulation weight and encapsulation thickness, respectively. Validation tests were performed. The test results were compared with approaches based on statistical regression, neural network and fuzzy regression. From a comparison of the results, it can be concluded that among these the TS neural fuzzy system is the best approach for modeling fluid dispensing.

The aggregation of multiple three-way decision spaces

Based on the theory of three-way decisions proposed by Yao, Hu established three-way decision spaces on fuzzy lattices and partially ordered sets. At the same time, multiple three-way decision spaces and its corresponding three-way decisions were also established. How to choose a method for the transformation from multiple three-way decision spaces to a single three-way decision space? This is one of the main problems on multiple three-way decision spaces. In connection with the transformation question on multiple three-way decision spaces, this paper gives out an aggregation method from multiple three-way decision spaces to a single three-way decision space through an axiomatic complement-preserving aggregation function. These aggregation methods in the partially set 0,1 contain the weighted average three-way decisions, max-min average three-way decisions and median three-way decisions etc. These methods are generalized to three-way decisions over two groups of multiple three-way decision spaces. At last we illustrate aggregation methods of multiple three-way decision spaces through a practical example.

Determining when to update the weights in combined forecasts for product demand--an application of the CUSUM technique

Abstract Combining forecasts merges several separate sets of forecasts to form a better composite forecast. There has been much published work on how to find the optimal combining weights. Several authors have suggested that changing the weights from time to time would be better than using fixed weights (FW). The unresolved problem is when to change the weights, on a regular basis or otherwise. The aim of this paper is to use the techniques of quality control to decide when we need to change the combining weights. An efficient and simple method to control the weights of the combined forecast is proposed and shown to perform better than one based on FW.

Sequential variable sampling plan for normal distribution

Abstract In this paper, a sequential variable sampling plan is studied. Suppose that the quality of an item in a batch is measured by a normally distributed random variable with a known variance, but the mean is unknown with a normal prior distribution. Then by using Bayesian approach and considering a Markov decision process, the optimality equations for the minimum total expected cost are formulated. We show that an optimal decision rule will have a control limit structure. An algorithm for a sequence of ϵ -optimal decisions is introduced. Then, the statistical procedure for conducting the sequential sampling plan is presented.