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EMPIRICAL EVIDENCE FOR ADAPTIVE CONFIDENCE INTERVALS AND IDENTIFICATION OF OUTLIERS USING METHODS OF TRIMMING
Author(s) -
CLARKE BRENTON R.
Publication year - 1994
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1994.tb00637.x
Subject(s) - studentized range , trimming , confidence interval , studentized residual , statistics , outlier , mathematics , robust confidence intervals , statistic , cdf based nonparametric confidence interval , range (aeronautics) , point estimation , credible interval , econometrics , standard deviation , computer science , engineering , aerospace engineering , operating system
Summary In an attempt to apply robust procedures, conventional t‐tables are used to approximate critical values of a Studentized t‐statistic which is formed from the ratio of a trimmed mean to the square root of a suitably normed Winsorized sum of squared deviations. It is shown here that the approximation is poor if the proportion of trimming is chosen to depend on the data. Instead a data dependent alternative is given which uses adaptive trimming proportions and confidence intervals based on trimmed likelihood statistics. Resulting statistics have high efficiency at the normal model, proper coverage for confidence intervals, yet retain breakdown point one half. Average lengths of confidence intervals are competitive with those of recent Studentized confidence intervals based on the biweight over a range of underlying distributions. In addition, the adaptive trimming is used to identify potential outliers. Evidence in the form of simulations and data analysis support the new adaptive trimming approach.