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Multivariate Density Estimation and Visualization

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  • Scott, David W.

Abstract

This chapter examines the use of flexible methods to approximate an unknown density function, and techniques appropriate for visualization of densities in up to four dimensions. The statistical analysis of data is a multilayered endeavor. Data must be carefully examined and cleaned to avoid spurious findings. A preliminary examination of data by graphical means is useful for this purpose. Graphical exploration of data was popularized by Tukey (1977) in his book on exploratory data analysis (EDA). Modern data mining packages also include an array of graphical tools such as the histogram, which is the simplest example of a density estimator. Exploring data is particularly challenging when the sample size is massive or if the number of variables exceeds a handful. In either situation, the use of nonparametric density estimation can aid in the fundamental goal of understanding the important features hidden in the data. In the following sections, the algorithms and theory of nonparametric density estimation will be described, as well as descriptions of the visualization of multivariate data and density estimates. For simplicity, the discussion will assume the data and functions are continuous. Extensions to discrete and mixed data are straightforward.

Suggested Citation

  • Scott, David W., 2004. "Multivariate Density Estimation and Visualization," Papers 2004,16, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    • Handle: RePEc:zbw:caseps:200416
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    1. B. W. Silverman, 1982. "Kernel Density Estimation Using the Fast Fourier Transform," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(1), pages 93-99, March.
    2. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
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    1. Ouafae Benrabah & Elias Ould Saïd & Abdelkader Tatachak, 2015. "A kernel mode estimate under random left truncation and time series model: asymptotic normality," Statistical Papers, Springer, vol. 56(3), pages 887-910, August.
    2. Sayed A. Mostafa & Ibrahim A. Ahmad, 2019. "Kernel density estimation from complex surveys in the presence of complete auxiliary information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(3), pages 295-338, April.
    3. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR scenarios with product beta distributions," Papers 1808.02457, arXiv.org, revised Jan 2019.
    4. Dietmar Pfeifer & Andreas Mandle & Olena Ragulina & C^ome Girschig, 2018. "New copulas based on general partitions-of-unity (part III) - the continuous case (extended version)," Papers 1803.00957, arXiv.org, revised May 2019.

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