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A regression smoother for resistant measures of location and scale
Author(s) -
Wilcox Rand R.
Publication year - 1995
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1995.tb01057.x
Subject(s) - estimator , outlier , scale (ratio) , measure (data warehouse) , mathematics , statistics , truncated mean , function (biology) , transformation (genetics) , nonparametric statistics , computer science , regression , variable (mathematics) , econometrics , feature (linguistics) , data mining , chemistry , linguistics , philosophy , quantum mechanics , evolutionary biology , biology , gene , mathematical analysis , biochemistry , physics
There are a variety of exploratory and informal graphical methods for studying the relationship between two random variables, many of which offer some resistance to outliers or unusual values. Some of these are extremely flexible when considering how the mean of Y might be related to some other random variable, X . However, when interest is focused on a resistant measure of location, such as the trimmed mean or a robust M‐estimator of location, the choice of methods is considerably reduced, and some of the more obvious procedures can fail. When dealing with how a measure of scale associated with Y varies as a function of X , even fewer methods arc available. This paper suggests a simple exploratory procedure that can be used to study how any parameter associated with Y varies as a function of Moreover, this is done without imposing any restrictions on what the relationship might be. The method might be used to suggest an appropriate transformation of the data, to summarize data without imposing any parametric restrictions, and in some cases the method suggests pursuing an investigation where more standard techniques (correlation and least squares regression) suggest that there is nothing interesting in the data. This latter feature is illustrated with data from a study on when a child utters its first word.