Bovas Abraham

Taguchi's parameter design: a panel discussion

It is more than a decade since Genichi Taguchis ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchis methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchis methodology for implementing it. The topics covered include the importance of vari...

Adjusted Empirical Likelihood and its Properties

Computing a profile empirical likelihood function, which involves constrained maximization, is a key step in applications of empirical likelihood. However, in some situations, the required numerical problem has no solution. In this case, the convention is to assign a zero value to the profile empirical likelihood. This strategy has at least two limitations. First, it is numerically difficult to determine that there is no solution; second, no information is provided on the relative plausibility of the parameter values where the likelihood is set to zero. In this article, we propose a novel adjustment to the empirical likelihood that retains all the optimality properties, and guarantees a sensible value of the likelihood at any parameter value. Coupled with this adjustment, we introduce an iterative algorithm that is guaranteed to converge. Our simulation indicates that the adjusted empirical likelihood is much faster to compute than the profile empirical likelihood. The confidence regions constructed via the adjusted empirical likelihood are found to have coverage probabilities closer to the nominal levels without employing complex procedures such as Bartlett correction or bootstrap calibration. The method is also shown empirical likelihood.

Some risks in the construction and analysis of supersaturated designs

A designed experiment in which the number of factors is at least as large as the number of runs is referred to as a supersaturated (SS) design. Recently these designs have received increased attention. Construction of such designs and analysis of data from them have been discussed by several authors. Our objective in this article is to examine these designs and methods for their analysis. An important finding for practitioners is that the correlation structure inherent in SS designs can obscure real effects or promote nonreal effects. Whatever analysis method is used, this problem can occur, although all-subsets regression is preferable to stepwise regression. Hence, one should be cautious with the use of SS designs.

Outlier detection and time series modeling

Some statistics used in regression analysis are considered for detection of outliers in time series. Approximations and asymptotic distributions of these statistics are considered. A method is proposed for distinguishing an observational outlier from an innovational one. A four-step procedure for modeling time series in the presence of outliers is also proposed, and an example is presented to illustrate the methodology.

Intervention analysis and multiple time series

SUMMARY A general model is introduced to encapsulate interventions in a rnultiple time series. The estimation of this model is discussed, and a bivariate economic example is presented to illustrate the methods.

Deterministic and Forecast-Adaptive Time-Dependent Models

Some concern has been expressed in the past as to whether the Autoregressive Integrated Moving Average (arima) time series models might wrongly be employed where “deterministic” ones would be more appropriate. The fact is that for a wide class of functions the arima models are capable of indicating the need for “deterministic” components if they are there. This need is shown by a near cancellation of operators in the difference equation model and yielding a non‐adaptive complementary function for the difference equation.

Parsimony and Its Importance in Time Series Forecasting

The effect of nonparsimonious time series models is studied by deriving the approximate variance of the one-step-ahead forecast error. Also, in a simulation experiment we show the loss in forecast accuracy that can result when a first-order moving-average model is approximated by a nonparsimonious autoregressive model.

Temporal Aggregation and Time Series

Summary Often business or economic data are available in temporally aggregated form. In this paper we discuss how the models for the aggregates suggested by the disaggregated data compare with those directly obtained from the aggregates. Using post sample predictions and actual data we also investigate the efficiency of forecasting future aggregates using a series of aggregates rather than disaggregates.

Forecasting contemporal time series aggregates

Forecast of a contemporal aggregate of several time series can be obtained from ‘1’ an aggregate series, ‘2’ individual component processes, or ‘3’ a joint multiple forecasting model. Through general Hilbert space theory and some illustrative examples, this paper establishes the relative efficiencies among the three methods

Missing observations in time series

A method based on forecasting techniques is proposed to estimate missing observations in time series. Using mean squares, this method is compared to the minimum mean square estimate.