INFLUENCE DIAGNOSTICS IN MULTIVARIATE METHODS : LOCAL INFLUENCE IN PCA AND STANDARDIZATION OF INFLUENCE FUNCTIONS WITH A CONTINUOUS ARGUMENT IN FUNCTIONAL DATA ANALYSIS

DOI Web Site 24 References
  • Tanaka Yutaka
    Department of Environmental & Mathematical Sciences, Okayama University

Bibliographic Information

Other Title
  • 多変量解析における影響診断 : PCAの局所影響とFDAにおける影響関数の標準化
  • タヘンリョウ カイセキ ニ オケル エイキョウ シンダン PCA ノ キョクショ エイキョウ ト FDA ニ オケル エイキョウ カンスウ ノ ヒョウジュンカ

Search this article

Description

The present paper reviews recent researches on influence diagnostics in multivariate methods, which deal with the evaluation of the influence of observations on the results of analysis or the detection of singly and/or jointly influential observations, and discusses two topics in details. The first topic is Cook's local influence in PCA and its relationship with our multiple-case diagnostics based on the influence function approach . Here the local influence is derived where the parameters of interest are contained in equality contraints but not in the likelihood function. So far the local influence has been derived in the cases where the parameters of interest are contained in the likelihood functions. But, as shown in PCA, the local influence can be derived not only in the cases where the parameters of interest are contained in the likelihood functions but also in the cases they are contained in equality contraints. The equivalence holds between the results of the local influence approach and the results of multiple-case diagnostics in the influence function approach. The second topic is how to standardize the influence functions with a continuous argument such as the influence functions of weight functions in the functional data analysis. We transform such continuous influence functions to discrete influence functions by sampling from the range of the continuous argument with appropriate intervals, and then apply Mahalanobis-type standardization. Our basic idea is to define the standardization in the continuous case as the limit when the intervals approach zero and the number of sampling tends to infinity. We can prove that when the number of sampled points is larger than a certain number, the statistics in the multiple-case as well as single-case diagnostics become constant and the values are the same with the results when we apply influence diagnostics to the coefficient vectors of the basis function expansions.

Journal

References(24)*help

See more

Keywords

Details 詳細情報について

Report a problem

Back to top