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1986•Statistica NeerlandicaRequires access

PERFORMANCE OF STUDENTIZED RANGE STATISTIC FOR TWO OUTLIERS IN A LINEAR MODEL

S. Lalitha, Prakash Joshi

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Abstract

Abstract. In JOSHI and LALITHA (1986) a statistic K is proposed for detecting two outliers present in the opposite directions in a linear model. This statistic reduces to the Studentized range statistic for the case of a simple random sample from a normal population. In this paper, the performance of this statistic is studied. For this an approximate non–null density of the random variables involved in defining the statistic is derived. An exact density is also obtained by using the methods of LALITHA and JOSHI (1986), where the results are proved for Murphy's statistic. A measure of performance is then defined and an example is also given for highlighting the usage of the above said statistic.

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What this paper is about

Abstract. In JOSHI and LALITHA (1986) a statistic K is proposed for detecting two outliers present in the opposite directions in a linear model. This statistic reduces to the Studentized range statistic for the case of a simple random sample from a normal population. In this paper, the performance of this statistic is studied. For this an approximate non–null density of the random variables involved in defining the statistic is derived. An exact density is also obtained by using the methods of LALITHA and JOSHI (1986), where the results are proved for Murphy's statistic. A measure of performance is then defined and an example is also given for highlighting the usage of the above said statistic.

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Available abstract

Abstract. In JOSHI and LALITHA (1986) a statistic K is proposed for detecting two outliers present in the opposite directions in a linear model. This statistic reduces to the Studentized range statistic for the case of a simple random sample from a normal population. In this paper, the performance of this statistic is studied. For this an approximate non–null density of the random variables involved in defining the statistic is derived. An exact density is also obtained by using the methods of LALITHA and JOSHI (1986), where the results are proved for Murphy's statistic. A measure of performance is then defined and an example is also given for highlighting the usage of the above said statistic.

Key concepts: Studentized range, Statistic, Mathematics, PRESS statistic, Outlier, Statistics, Ancillary statistic, Range (aeronautics)

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