書誌事項
- タイトル別名
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- ヘイキン 2ジョウ ゴサ シヒョウ ニ ヨル リッジパラメータ ニ カンスル エイキョウリョク ヒョウカ
- Using the Mean Square Error Index to Assess the Influence of the Ridge Parameter
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type:Article
Several influence measures have been proposed to assess the influence of observations on ridge regression. Influence measures based on the case deletion procedure that are used in the case of linear regression, such as Cook's distance or the likelihood distance, have been extended to the case of ridge regression. Most of these influence measures are derived from benchmarks based on statistical or mathematical distance criteria. In the case of a typical linear regression, these measures are the primary methods for conducting such assessments. However, in the case of ridge regression, we must consider not only assessments of the influence of observations but also assessments of the influence of the ridge parameter, a feature unique to the case of ridge regression. Therefore, in the present paper, we consider an ancillary influence measure for the latter assessment. The present study is a detailed investigation of the properties of an ancillary influence measure derived from benchmarks based on the mean square error criterion. The mean square error criterion is a standard statistical benchmark used to assess the regression coefficients in ridge regression, and it is also frequently used to identify an optimal ridge parameter. To investigate the properties of this ancillary influence measure, we derive a derivative function by computing partial derivatives with respect to the ridge parameter. As a result of this investigation, we discovered that the derivative function may be expressed as the sum of the original function and functions associated with it. In addition, we plot the behavior of the derivative function for each observation in order to obtain a clear understanding of variations with respect to the ridge parameter. Our results demonstrate that assessments of the influence of the ridge parameter are a useful, albeit ancillary and supplemental, complement to the case deletion procedure for assessing the influence of observations.
identifier:0495-8012
identifier:https://repository.tku.ac.jp/dspace/handle/11150/6522
収録刊行物
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- 人文自然科学論集 = The Journal of Humanities and Natural Sciences
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人文自然科学論集 = The Journal of Humanities and Natural Sciences 135 57-70, 2014-03-20
東京経済大学人文自然科学研究会
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詳細情報 詳細情報について
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- CRID
- 1050001337487391232
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- NII論文ID
- 120005437259
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- NII書誌ID
- AN00159446
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- ISSN
- 04958012
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- NDL書誌ID
- 025613839
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- 本文言語コード
- ja
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
- NDL
- CiNii Articles