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Error Distribution for Gene Expression Data

Author

Listed:
  • Purdom Elizabeth

    (Stanford University)

  • Holmes Susan P

    (Stanford University)

Abstract

We present a new instance of Laplace's second Law of Errors and show how it can be used in the analysis of data from microarray experiments. This error distribution is shown to fit microarray expression data much better than a normal distribution. The use of this distribution in a parametric bootstrap leads to more powerful tests as we show that the t-test is conservative in this setting. We propose a biological explanations for this distribution based on the Pareto distribution of the variables used to compute the log ratios.

Suggested Citation

  • Purdom Elizabeth & Holmes Susan P, 2005. "Error Distribution for Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-35, July.
    • Handle: RePEc:bpj:sagmbi:v:4:y:2005:i:1:n:16
    DOI: 10.2202/1544-6115.1070
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    Citations

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    Cited by:

    1. Kaul, Abhishek & Koul, Hira L., 2015. "Weighted ℓ1-penalized corrected quantile regression for high dimensional measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 72-91.
    2. Tomy, Lishamol & Jose, K.K., 2009. "Generalized normal-Laplace AR process," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1615-1620, July.
    3. Punathumparambath, Bindu & Kulathinal, Sangita & George, Sebastian, 2012. "Asymmetric type II compound Laplace distribution and its application to microarray gene expression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1396-1404.
    4. Arslan, Olcay, 2009. "Maximum likelihood parameter estimation for the multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2158-2165, October.
    5. Mehmet Niyazi Çankaya & Abdullah Yalçınkaya & Ömer Altındaǧ & Olcay Arslan, 2019. "On the robustness of an epsilon skew extension for Burr III distribution on the real line," Computational Statistics, Springer, vol. 34(3), pages 1247-1273, September.
    6. Chenguang Wang & Ao Yuan & Leslie Cope & Jing Qin, 2022. "A semiparametric isotonic regression model for skewed distributions with application to DNA–RNA–protein analysis," Biometrics, The International Biometric Society, vol. 78(4), pages 1464-1474, December.
    7. Tu, Shiyi & Wang, Min & Sun, Xiaoqian, 2016. "Bayesian analysis of two-piece location–scale models under reference priors with partial information," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 133-144.
    8. Huixia Judy Wang & Leonard A. Stefanski & Zhongyi Zhu, 2012. "Corrected-loss estimation for quantile regression with covariate measurement errors," Biometrika, Biometrika Trust, vol. 99(2), pages 405-421.
    9. Tsai, Arthur C. & Liou, Michelle & Simak, Maria & Cheng, Philip E., 2017. "On hyperbolic transformations to normality," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 250-266.
    10. Salas-Gonzalez, Diego & Kuruoglu, Ercan E. & Ruiz, Diego P., 2009. "A heavy-tailed empirical Bayes method for replicated microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1535-1546, March.
    11. Lama, Nicola & Boracchi, Patrizia & Biganzoli, Elia, 2009. "Exploration of distributional models for a novel intensity-dependent normalization procedure in censored gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1906-1922, March.
    12. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.
    13. Kelmansky Diana M. & Martínez Elena J. & Leiva Víctor, 2013. "A new variance stabilizing transformation for gene expression data analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 653-666, December.
    14. Qin Li-Xuan & Satagopan Jaya M, 2009. "Normalization Method for Transcriptional Studies of Heterogeneous Samples - Simultaneous Array Normalization and Identification of Equivalent Expression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-23, February.
    15. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.

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