Various Types of Nonparametric Transformation and Its Diagnosis

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  • Ito Masanori
    Biometrics Depertment, Drug Development Devision, Yamanouchi Pharmaceutical Co., Ltd.,
  • Goto Masashi
    Division of Statistical Science, Graduate School of Engineering Sciences, Osaka University

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Other Title
  • ノンパラメトリック変換の諸型と診断
  • ノンパラメトリック ヘンカン ノ ショケイ ト シンダン

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Description

In this paper, we introduce a Nonparametric Transform-Both-sides (NTB) approach as an alternative to the Power Transform-Both-sides (PTB) approach to inference for theoretical models and propose a method of parameter estimation by expressing the function transformation as a cubic spline curve. From the investigation of two examples, we suggest that the NTB could be an index for the validation of the PTB and is more robust than PTB to outliers. Furthermore, we verify these results by three simulation experiments. In the methodology for fitting the empirical model, we introduce Alternating Conditional Expectation (ACE) and Additivity VAriance Stabilization (AVAS) as two nonparametric transformation approaches that optimize the relationship between response and explanatory variables. We examine the validity of the theoretical models by fitting empirical models via ACE and AVAS to the example data. Both method, ACE and AVAS, improve the normality and homoscedasticity of the error.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 33 (1), 3-26, 2004

    Japanese Society of Applied Statistics

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