Talk:Kernel density estimation

message: At the section Example, the text was claiming using variance 2.25, when in fact it is referring to standard deviation (I also suspect it should have been 2.5 instead of 2.25, since 2.25 creates a barely noticeable deviation at the graph, but only the figure author may confirm). I've fixed the term (see Image for justification), yet, in accordance with formula at section Definition, it should also be an average as stated below. 
  — Preceding unsigned comment added by Rafael Siqueira Telles Vieira (talk • contribs) 16:37, 25 October 2019 (UTC)
thread_title: Misusage of the word variance

message: Note that the figure shows
\sum_{i=1}^N W(x-x_i)
rather than
\frac{1}{N}\sum_{i=1}^N W(x-x_i)
as the caption says. --anon
:How do you know, as there is no y-axis in the picture? Oleg Alexandrov (talk) 03:31, 1 March 2006 (UTC)
replies: text: \frac{1}{N}\sum_{i=1}^N is an average.  An average is never greater than the largest component.  If you look at the graph, the blue curve is clearly the sum of the component curves. Zik 03:40, 5 March 2006 (UTC)
replies: text:  You are right, I fixed the caption. I have no idea how I had missed that. :) Oleg Alexandrov (talk) 01:09, 6 March 2006 (UTC)
thread_title: Incorrect caption

message: In my experience calling the technique Parzen windowing is limited specifically to time-series analysis, and mainly in engineering fields.  In general statistics (and in statistical machine learning), the term kernel density estimation is much more common.  Therefore I'd propose it be moved there.  As an aside, the attribution to Parzen is also historically problematic, since Rosenblatt introduced the technique into the statistics literature in 1956, and it had been used in several more obscure papers as early as the 1870s, and again in the early 1950s. --Delirium 22:59, 26 August 2006 (UTC)
thread_title:  name 

message: What is x in the equation? --11:06, 5 October 2006 (UTC)
replies: text: It is a real number, I guess. Oleg Alexandrov (talk) 02:55, 6 October 2006 (UTC)
thread_title:  x 

message: The technique called here Parzen window is called kernel density estimation in non parametric statistics. It seems to me to be a much more general term and much clearer for people searching for it. The comment above state the same problem. I also agree that the article should refer to the Parzen-Rosenblatt notion of a kernel, and not just of Parzen. The definition of a Parzen-Rosenblatt kernel should be latter added on the kernel (statistics) page. —The preceding unsigned comment was added by Gpeilon (talk • contribs).
: That's fine with me. If you move the page, you should also fix the double redirects. That is, after the move, while viewing the article at the new name, click on "what links here" on the left, and any redirects which point to redirects need to be made to point to the new name. Cheers, Oleg Alexandrov (talk) 03:18, 9 January 2007 (UTC)
thread_title: Changing the name of this page

message: Hi,
I just noticed that the optimal global bandwidth in
Rosenblatt, M. The Annals of Mathematical Statistics, Vol. 42, No. 6. (Dec., 1971), pp. 1815-1842.
has an additional factor of 2^{\frac{2}{5}}. Just an oversight, or is there a reason for the difference that I'm missing? Best, Yeteez 18:34, 24 May 2007 (UTC)
replies: text: n is the same as N, and is the amount of data samples. I changed it in the Definition section from N to n to avoid confusion. 78.21.160.201 (talk) 12:50, 27 August 2009 (UTC)
thread_title: Formula for optimal bandwidth

message: Shouldn't the \sigma in the formula for K(x) be dropped, on the grounds that it is already there in the form of h in the formula for \hat{f}_h(x)?
--Santaclaus 15:45, 7 June 2007 (UTC)
thread_title: Scaling factor

message: Though not sure whether it violates the guidelines of what wikipedia is, I like the example section. But I would like to see the commands in some non-proprietory language, e.g. R. --Ben  T/C  14:41, 2 July 2007 (UTC)
thread_title:  [[Stata]] 

message: Isn't a Gaussian with variance of 1 totally arbitrary? On the other hand, using the PDF of your measurement tool as a kernel seems quite meaningful. For example, if you are measuring people's heights and know you can measure to a std. dev of 1/4", then convolving the set of measured heights by a Gaussian with std. dev of 1/4" seems like it captures everything you know about the data set. For example, in the limit of one sample, the estimation would reflect our best guess of the distribution for that one person. 155.212.242.34 22:07, 6 November 2007 (UTC)
replies: text: Anybody? —Ben FrantzDale (talk) 16:00, 26 August 2008 (UTC)
thread_title:  Kernel? 

message: It appears that the section Properties tells us how to select h.  However, I found several things confusing here, and would like to see these described more clearly.
First, if I'm interpreting correctly, c_1 and c_2 would be constants for the standard normal kernel that was earlier stated to be the common choice, e.g. c_1=1 and c_2\approx0.28.  The fact that these constants for the standard normal were not given confused me and left me thinking that maybe there was a notational inconsistency or something, or that I wasn't interpreting something right.  So please, mention what these constants are for the standard kernel choice.
Next and more serious, I'm still confused about c_3.  It appears that we're going to find c_3 in order to find h^*  But c_3 apparently must be estimated as a function of h.  I mean if f is the underlying true distribution, which we don't know, then we don't know f(x), so the implication is that we'd need to use  \hat f, which is defined in terms of h.  So it seems like h^* has a circular definition.  —Preceding unsigned comment added by 98.207.54.162 (talk) 19:12, 7 February 2009 (UTC)
replies: text: You are correct. I added an internal link about c_1 and c_2 to the relevant page. For c_3 somebody with more knowledge of the estimation algorithms (cross-validation, plug-in etcetera) should have a look, as none of those algorithms are presently discussed on wikipedia. In any case the parameter c_3 must be estimated from the input data set, and is usually derived from its variance \sigma^2. Probably something should be said about the derivation of the R(f,\hat f(x)) function as well, which is (I think) the AMISE form. 78.21.160.201 (talk) 12:44, 27 August 2009 (UTC)
thread_title:  Properties section - more on <math>c_1, c_2, c_3</math> 

message: The description of a histogram as KDE with a boxcar kernel is not entirely accurate.  In a histogram the bin centers are fixed, whereas in KDE the kernel is centered on each data point.  See this page for more explanation.  --Nubicles (talk) 04:19, 20 February 2009 (UTC)
thread_title:  Comparison to histogram 

message: a) Discussion of boundary effects. These effects are important in many practical applications. Statements in the article about optimal AMISE rates are incorrect in the presence of boundary bias.
b) High-order kernels. If you are willing to assume that the kernel is not necessarily positive, these should be mentioned. Again, statements in the article about optimal AMISE rates are incorrect if high-order kernels are allowed (these kernels lead to better asymptotic convergence rates).  — Preceding unsigned comment added by 95.32.237.124 (talk) 22:23, 19 August 2011 (UTC)
thread_title:  Things that are missing 

message: Maybe if someone could check :
h    <- hpi(x=waiting)
function hpi is not accesable (maybe removed)
plot(fhat, drawpoints=TRUE)
drawpoints is not longer a parameter   — Preceding unsigned comment added by 143.169.52.102 (talk) 09:45, 14 August 2012 (UTC)
thread_title:  Error in R-code fragment 

message: This article mentions: “after [Emanuel Parzen] and [Murray Rosenblatt], who are usually credited with independently creating it in its current form”. This is not correct. Parzen refers to Rosenblatt (so clearly NOT independent, and btw both papers are in the same journal), and the paper of Parzen does not provide the simple equations that we find in this paper.
If there is no objection, I'd like to correct this. Phdb (talk) 22:08, 25 September 2011 (UTC)
replies: text: Parzen wrote: "Despite the obvious importance of these problems, we are aware of only two previous papers on the subject of estimation of the probability density function (Rosenblatt [5] and Whittle [6]). In this paper we show how one may construct a family of estimates of f(x), and of the mode, which are consistent and asymptotically normal."  It's still not clear to me exactly who did what, or who is credited with what, but I'd rather go be a secondary source on that.  Dicklyon (talk) 05:49, 20 June 2014 (UTC)
thread_title:  Error in reference about origin 

message: The first sentence says "In statistics, kernel density estimation (KDE) is a **non-parametric** way to estimate the probability density function of a random variable." Then further down is: "The bandwidth of the kernel is a **free parameter** which exhibits a strong influence on the resulting estimate."  So which is it?  — Preceding unsigned comment added by 115.187.246.104 (talk) 10:05, 3 June 2014 (UTC)
replies: text: I think the point is that the method is not estimating a parameter that describes a distribution.  There is a free parameter in the choice of window, but given a window, the density estimate is nonparametric, determined directly by the data without parameters limiting the shape.  Dicklyon (talk) 05:53, 20 June 2014 (UTC)
thread_title:  Parameteric or non-parametric? 

message: "K(•) is the kernel — a symmetric but not necessarily positive function that integrates to one"
Shouldn't it be the exact opposite: "K(•) is the kernel — a positive but not necessarily symmetric function that integrates to one"?
--Lucas Gallindo (talk) 21:40, 18 October 2014 (UTC)
thread_title:  Definition - symmetric but not necessarily positive 

message: Dr. Guillen has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Guillen has published scholarly research which seems to be relevant to this Wikipedia article:
*Reference : Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referencia en Economia Aplicada (XREAP), revised Oct 2012.
ExpertIdeasBot (talk) 06:47, 8 July 2015 (UTC)
thread_title:  Dr. Guillen's comment on this article 

message: This section starts off with an incorrect claim:
> Kernel density estimation may have certain limitations because it is based on Gaussian distribution statistics
There are KDE methods that use the Gaussian distribution as a starting point (pilot estimator). There are KDE methods that use Gaussian kernels. These are not necessary or exhaustive choices. There are also KDE methods for heavy-tailed distributions, such as variable bandwidth KDE and data transformations.
Then there is the unsupported claim:
> In this connection, head/tail breaks[27] and its deduced TIN-based density estimation[28] can better characterize the heavy-tailed data.
Looking at the two references on the ArXiv, how can you say that the TIN method better characterizes a certain kind of data when (1) you never compared method TIN to KDE (nether paper mentions KDE) and (2) have not worked out the statistical properties of method TIN (not published in a stats journal btw)?
---(192.161.76.82 (talk))  —Preceding undated comment added 23:06, 18 October 2017 (UTC)
thread_title:  Alternative methods 

message: I guess it must be "Intuitively one wants to choose h as large as the data will allow" in the Definition section, because you can let go h to zero, achieving a perfect fit between data and probability density (sum of delta functions). Am I right or wrong?Syspedia (talk) 10:12, 16 November 2017 (UTC)
thread_title:  Minor correction of wording 

message: Histogram bin edges need to be defined: -4, -2, 0, ..., 8.
Also, if there are 6 data points, why are the bars 1/12 high?  — Preceding unsigned comment added by 2600:1700:EB40:86D0:707F:873F:613E:BAB8 (talk) 00:01, 18 December 2021 (UTC)
thread_title: Histogram example errors

message: Tree-structured Parzen estimators link here, but shouldn't they have their own article? There is more to say, see here:
https://towardsdatascience.com/a-conceptual-explanation-of-bayesian-model-based-hyperparameter-optimization-for-machine-learning-b8172278050f Biggerj1 (talk) 21:04, 12 October 2022 (UTC)
thread_title:  Tree-structured Parzen estimators