In this chapter, we investigate and compare six distribution-free exponentially weighted moving average (EWMA) schemes for simultaneously monitoring the lo- cation and scale parameters of a univariate continuous process. More precisely, we consider a well-known distribution-free EWMA scheme based on the Lepage statis- tic, and we propose ve new EWMA schemes for the same purpose. One of the ve new schemes is based on the maximum of EWMA of two individual components, one for the location parameter and the other for the scale parameter, of the Lepage statistic. Such a component-wise combined EWMA is referred to as the cEWMA. Further, we consider an EWMA scheme based on the Cucconi test statistic. We show that it is possible to express the Cucconi statistic as a quadratic combina- tion of two orthogonal statistics, one of which is useful for monitoring the location parameter and the other for monitoring the scale parameter. Such decomposition of the Cucconi statistic is not unique, and one can split it in three dierent ways. Therefore, we design three more cEWMA schemes corresponding to the decompo- sitions of the Cucconi statistic. We discuss the implementation steps along with an illustration. We perform a detailed comparative study based on Monte-Carlo simulation. We observe that the three cEWMA-Cucconi schemes perform very well for various location-scale models.
A Class of Distribution-Free Exponentially Weighted Moving Average Schemes for Joint Monitoring of Location and Scale Parameters
M. Marozzi;
2020
Abstract
In this chapter, we investigate and compare six distribution-free exponentially weighted moving average (EWMA) schemes for simultaneously monitoring the lo- cation and scale parameters of a univariate continuous process. More precisely, we consider a well-known distribution-free EWMA scheme based on the Lepage statis- tic, and we propose ve new EWMA schemes for the same purpose. One of the ve new schemes is based on the maximum of EWMA of two individual components, one for the location parameter and the other for the scale parameter, of the Lepage statistic. Such a component-wise combined EWMA is referred to as the cEWMA. Further, we consider an EWMA scheme based on the Cucconi test statistic. We show that it is possible to express the Cucconi statistic as a quadratic combina- tion of two orthogonal statistics, one of which is useful for monitoring the location parameter and the other for monitoring the scale parameter. Such decomposition of the Cucconi statistic is not unique, and one can split it in three dierent ways. Therefore, we design three more cEWMA schemes corresponding to the decompo- sitions of the Cucconi statistic. We discuss the implementation steps along with an illustration. We perform a detailed comparative study based on Monte-Carlo simulation. We observe that the three cEWMA-Cucconi schemes perform very well for various location-scale models.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
