Robust Change Point Estimator For Series Of Normal Observations

787 words - 4 pages

Change-point analysis started from a Bayesian point of view with Girshick and Rubin [2]. They defined a quality control rule which have to be applied after a change in a random process is detected. Page [3-5], from a frequentist point of view, developed a control chart based on cumulative sums: the cumulative sums (CUSUM) chart, which in presence of sustained changes are faster to detect them than traditional Shewhart’s control charts [6].

Hinkley [7] set the basis to construct maximum likelihood estimators (MLEs) and likelihood ratios tests (LRTs) from a parametric approach. These techniques were applied to independent and normally distributed observations. Following this guideline, MLEs ...view middle of the document...

On the other hand, from a non-parametric approach, Page [4] proposed a method using the sign function to determine changes in the mean of symmetrical distributions. Later, Bhattacharyya and Johnson [19] developed a test assuming symmetry of the cumulative distribution of the observations. Pettitt [20] work with Bernoulli, binomial and continuous observations proposing test the null hypothesis of no change and obtaining approximations and exact results of testing this hypothesis, and a year after, Pettitt [17] proposed a test based on the CUSUM previously developed by Page [4], for zero-one observations. Boostrap technique was used by Hinkley and Schechtman [21] to compare both parametric and non-parametric methods for shifts in the mean. In 2007, Zou et al. [22] solve the issue of the estimation of the change-point and the estimation by proposing the use of the empirical likelihood ratio. Recently, Tercero et al. [23] assessed the problem of estimating changes in time series using p-values of a non-parametric test: Mood’s median test.

Parametric approach for change-point estimation may present a higher bias in presence of outliers. In normal processes change-point MLE have the form of least-squares estimators (LSE). For estimation of parameters in regression models besides of LSE least absolute deviations estimators (LAD) are used to provide better estimations in the presence of outliers. This method estimates regression parameters by minimizing the sum of the...

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