1
$\begingroup$

I'm looking for references on the known issues that arise when working with histograms, i.e.: the choice of the number of bins, and the choice of the origin point.

The WP entry on Multivariate kernel density estimation points to Density Estimation for Statistics and Data Analysis, Bernard. W. Silverman (1986).

This book comments briefly on these issue in Sect. 2.2 (see below). Is there some other "canonical" reference for this topic or should this one suffice?


Pages 10-11 from Silverman (1986). Copyrighted material.

enter image description here

$\endgroup$
  • 1
    $\begingroup$ I get "Restricted Page - You have reached your viewing limit for this book". What did it say? Please include a quote of the most relevant parts $\endgroup$ – Glen_b -Reinstate Monica Apr 13 '16 at 9:41
  • $\begingroup$ Must be some country restriction. I am not allowed to copy/paste text in the book since it's disabled. I'll paste some images from the relevant pages. $\endgroup$ – Gabriel Apr 13 '16 at 12:51
  • $\begingroup$ If it's only a few sentences, simply type it in as a quote. $\endgroup$ – Glen_b -Reinstate Monica Apr 13 '16 at 13:16
  • $\begingroup$ @Glen_b should I remove the images from the pages I posted? $\endgroup$ – Gabriel Apr 13 '16 at 13:27
  • $\begingroup$ For the sake of completeness, this great answer by Glen mentions such issues stats.stackexchange.com/a/51753/10416, but no book or article to serve as reference is given. $\endgroup$ – Gabriel Apr 13 '16 at 14:50
2
$\begingroup$

I decided to go looking for a particular paper that I saw briefly, probably at least a decade ago, since it would be relevant (to my recollection it discusses issues with the impact of bin width on the impression of shape with a striking example that looks sort of exponential at one bin width and not exponential with another) but I couldn't find it. In searching for it, I did come across a few things though, including:

  1. Jeffrey S. Simonoff (1996) Smoothing Methods in Statistics Sec 2.4 (in particular p28 and 29 including figure 2.8 discusses the effect of changing bin anchor

    Also see

    Simonoff, J. S. and Udina, F. (1997),
    "Measuring the stability of histogram appearance when the anchor position is changed",
    Computational Statistics and Data Analysis, 23, (1997), pp. 335-353,
    http://hdl.handle.net/10230/655

    Besides discussing bin anchor (bin origin), it also looks to have at least some discussion of bin width; fairly technical. Figure 1 in that papershows the impact of changing bin origin on a data example

  2. The 2004 book by Härdle, Müller, Sperlich, and Werwatz, Nonparametric and Semiparametric Models discusses the effect of bin origin - Figure 2.3 shows an example of the effect of changing binwidth and section 2.3 discusses the effect of changing bin origin.

    Härdle, W., Müller, M., Sperlich, S., & Werwatz, A. (2004). Nonparametric and Semiparametric Models. New York: Springer Series in Statistics, Springer

    and closely related to that,

    Marlene Müller (2010),
    "Exploring data with non- and semiparametric models."
    ICOTS8 Invited paper,
    http://iase-web.org/documents/papers/icots8/ICOTS8_4B3_MULLER.pdf

    also has a similar brief discussion and figure 1 shows the effect in an example

  3. Keith N. Sircombe (2004),
    "AgeDisplay: an EXCEL workbook to evaluate and display univariate geochronological data using binned frequency histograms and probability density distributions",
    Computers & Geosciences 30, 21–31

    shows an effect on the appearance of histograms of changing bin width:

    The subtle variation in appearance and interpretation for a variety of bin widths is illustrated in Fig. 3. Although all the histograms show the age distribution is generally dispersive with two prominent modes (~2950 and ~3150 Ma), the relative prominence of the two modes change; this could alter interpretations about the relative importance of these modes.

  4. David C. LeBlanc (2004), Statistics: Concepts and Applications for Science, Vol. 2

    Figure 2.3 (Sec 2.2, p39) shows the effect on appearance of changing bin width on a histogram

$\endgroup$
  • $\begingroup$ Excellent list of resources Glen, thank you very much! $\endgroup$ – Gabriel Apr 14 '16 at 12:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.