Residual-based Approach Research Articles

Testing Conditional Asymmetry: A Residual-Based Approach

We propose three residual-based tests for conditional asymmetry. The distribution is assumed to fall into the class of skewed distributions of Fernandez and Steel (1998). In this class, asymmetry is measured by the ratio between the probabilities of being larger and smaller than the mode. Estimation is performed under the null hypothesis of constant asymmetry of the innovations and, in a second step, tests for conditional asymmetry are performed on generalized residuals through parametric and nonparametric methods. We derive the asymptotic distribution of the tests that incorporates the uncertainty of the estimated parameters in the first step. A Monte Carlo study shows that neglecting this uncertainty severely biases the tests and an empirical application on a basket of daily returns reveals that financial data often present dynamics in the conditional skewness.

Statistical process control for monitoring scheduling performance—addressing the problem of correlated data

In both manufacturing and service operations effective scheduling plays an important role in achieving delivery performance and in utilizing resources economically. Classical scheduling theory takes a narrow, static view of performance. In reality the assessment of scheduling performance is a particularly difficult task. Typically scheduling is an activity that takes place repeatedly over time in the context of an overall planning and control architecture. Scheduling may be viewed as an activity within a process. Statistical Process Control (SPC) provides an attractive option for monitoring performance. In this paper we investigate the potential of applying SPC control charts in this context. The feasibility of monitoring flow time in a single processor model using control charts is studied using simulation. The application of control charts to monitor time-related measures in operational systems raises fundamental statistical problems. The need for approaches that are robust with respect to data correlation and lack of normality is shown to be an essential requirement. Residual-based approaches and the Exponentially Weighted Moving Average (EWMA) chart are shown to be reasonably effective in avoiding false alarms and in detecting process shifts. The applicability of the single processor model to more complex operational systems is discussed. The implications of the work for the design of performance monitoring and continuous improvement systems for time-related measures in manufacturing and service operations are considered. A number of areas are highlighted for further theoretical and practical studies.

MULTIDIMENSIONAL UPWIND RESIDUAL DISTRIBUTION SCHEMES FOR THE CONVECTION-DIFFUSION EQUATION

SUMMARY Multidimensional residual distribution schemes for the convectiowdiffusion equation are described. Compact upwind cell vertex schemes are used for the discretization of the convective term. For the diffusive term, two approaches are compared the classical finite element Galerkin formulation, which preserves the compactness of the stencil used for the convective part, and various residual-based approaches in which the diffusive term, evaluated after a reconstruction step, is upwinded along with the convective term.

Adaptive collocation on finite elements models for the optimization of multistage distillation units

The size of the model for multistage distillation processes can be reduced by orthogonal collocation on finite elements (OCFE) techniques. The accuracy of the OCFE models can be improved by adaptively placing the breakpoints between the elements so that the approximation error is equally distributed among the elements within each column section. The location of the breakpoints depends on the features of the composition and temperature profiles in the column. Two different approaches are used for the estimation of the approximation error resulting from the OCFE solution. The first approach is based on the equidistribution of the residuals of the material and energy balances around envelopes that include predefined regions in the column. The additional constraints, generated by the adaptive grid procedure, are embedded into the economic optimization problem. Both the optimal operating conditions and the optimal breakpoint sequence are determined simultaneously. The second method uses the derivatives of the approximate solution and determines the element lengths by equidistributing the estimated error in an iterative procedure. The residual-based approach is more efficient than the derivative method in determining an element partition that results in a feasible optimal solution close to the optimal solution obtained by a tray-by-tray model. The adaptive placement of the breakpoints allows a more compact OCFE model for which an optimal solution exists. Multiple locally optimal element partitions may be obtained using the residual-based approach.