Loading...
Please wait, while we are loading the content...
Similar Documents
A Multivariate Parallelogram and Its Application to Multivariate Trimmed Means
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shiau, Jyh-Jen Horng Chen, Lin-An |
| Copyright Year | 2003 |
| Abstract | Let y1, . . . , yn denote a random sample from a univariate population with distribution function F, and let F̂ be the empirical distribution function obtained from this sample. Let Q(α1, α2) = (F(α1), F(α2)) denote the (α1, α2)-quantile interval of F and let Q̂(α1, α2) = (F̂(α1), F̂(α2)) denote the corresponding sample quantile interval, where F−1 and F̂−1 are the inverse functions of F and F̂ , respectively. The sample quantile interval plays a very important role in statistical inference. For example, as a region with a particular coverage probability, the interval is a natural estimator for scale parameters such as the range and interquartile range. With this property, the quantile interval can be used in industrial applications to define a process capability index for process capability assessment, especially for non-normal processes. Also, this interval is routinely used in classifying the observations of a sample into good or bad observations in robust mean estimation, such as for the trimmed mean and Winsorized mean. Analogues have been proposed for quantiles or order statistics in high dimensions. It is well known that the univariate quantile can be obtained by solving a minimization problem. Breckling & Chambers (1988) and Koltchinskii (1997) generalized the minimization problem for the multivariate case and then defined a multivariate quantile as the minimizer of the problem. Chaudhuri (1996) considered a geometric quantile that uses the geometry of multivariate data clouds. Chakraborty (2001) used a transformation-retransformation technique to introduce a multivariate quantile. However, these approaches do not have obvious settings for defining multivariate regions suitable for constructing descriptive statistics because they lack a natural ordering in multi-dimensional data. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ir.nctu.edu.tw/bitstream/11536/27600/1/000184955400007.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
