Questions tagged [trimmed-mean]

A k-trimmed mean is a mean where the largest and smallest k% of the observations are removed before the mean is calculated.

Filter by
Sorted by
Tagged with
3
votes
1answer
261 views

use and misuse of Winsorization

I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. ...
3
votes
1answer
64 views

If all trimmed means are equal does this imply equal distributions?

I am trying to prove the following: Given that $\forall \alpha\in [0,1]$: $$\int_{F_S^{-1}(\alpha)}^{\infty}xf_S(x)\,dx = \int_{F_0^{-1}(\alpha)}^{\infty}yf_0(y)\,dy$$ where $F_S^{-1}(\alpha)$ and $...
5
votes
2answers
735 views

An X% trimmed mean means?

Rand Wilcox in Fundamentals Of Statistical Methods, 1st. edition, gives a formula which says that for a 20% trimmed mean, you would trim away 20% of one end of the ranked data, and 20% of the other ...
0
votes
0answers
23 views

When is it better to exclude outliers and calculate the mean of the data instead of using the median?

I already searched on when to use the mean and median and I often see that median might be better than mean when the data is skewed, ordinal, include outliers, etc.. even tho, this might not be always ...
1
vote
0answers
72 views

Skewed data: Is trimming the means necessary when using bootstrapping to compare means?

I want to compare four different groups on one dependent variable. Normally I'd do a one-way independent ANOVA, except that this time the normality assumption isn't met at all (see the below ...
1
vote
0answers
71 views

Cumulative Moving Trimmed Mean [closed]

I would be interested in a technique to calculate the trimmed mean of a (potentially) infinite stream of observations. It is infeasible to store each of the observations and therefore, I have to ...
1
vote
1answer
585 views

Treatment of outliers in financial data

I have a data set with financial panel data from 150 companies. I want to analyse the data using linear repeated measures ANOVA and OLS Regression (so far). For this, I want to use the absolute values ...
5
votes
2answers
717 views

Mean vs. Trimmed mean in the normal distribution

In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the ...
3
votes
0answers
748 views

Downweight outliers in mean

I have a bunch of points $x_i$ and would like to calculate a kind of weighted mean that deemphasizes outliers. My first idea was to weight each point by $1/ (x_i - \mu)^2$. However, the problem is ...
2
votes
1answer
364 views

Does the Hodges-Lehmann estimator perform better than trimmed/winsorized means?

I've been reading about the HL estimator, and a question came to mind. I could fairly easily create a mean-estimator where I trim or clip 29% of the data on either side and have a statistic with a ...
1
vote
1answer
537 views

What is the difference between GAS ( Generalized Autoregressive Score) model and a GARCH?

I am trying to analyze some data about Brent Oil volatility. So far I have managed to fit a GARCH(1,1) model and an EGARCH. However, someone has recommended to use a GAS model, Generalized ...
3
votes
0answers
415 views

How to calculate a confidence interval for a trimmed mean

I try to get the sample size that presents the population, I averaged randomly the 10 and then the 20 readings then I used the formula CI = 1.96 * std/root n, that gave me the CI at any (n), but how ...
0
votes
0answers
346 views

Using trimmed means and Winsorized variances to compute standardisation of data

I am looking into the pros and cons of each normalisation technique for work and it got me thinking. What if I used trimmed means and the sqrt of Winsorized variances to compute the standardised data? ...
0
votes
0answers
83 views

Trimming, Winsorising and manipulating biological data

So I have an experiment with multiple groups (groups 1-6), individuals in each group (n=10), and read outs per individual. Eg. below Group 1: 28.1, 28.6, 29, 30.3,30.4,30.6,30.7,31.1.34 Group ...
5
votes
0answers
235 views

Sampling distribution of sample trimmed (truncated) mean

It is elementary probability theory that the sample mean of an i.i.d. sample follows normal distribution, if the background distribution is normal. But what about the trimmed mean? Is there any result ...
9
votes
2answers
5k views

Trimmed mean vs median

I have a data set with all the calls made to an emergency service and the response times of the ambulance department. They admitted that there are some mistakes with the response times as there are ...
0
votes
1answer
49 views

Trimmed mean for specific groups

I have a dataset with all the calls to an emergency service in a period of time. I have information about the time (in seconds) that it took to respond to that call and the area where the emergency ...
12
votes
3answers
714 views

How can I interpret a plot of trimming percentage vs. trimmed mean?

For part of a homework question, I was asked to calculate the trimmed mean for a dataset by deleting the smallest and largest observation, and to interpret the result. The trimmed mean was lower than ...
5
votes
1answer
488 views

Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by ...
3
votes
2answers
441 views

Modeling trimmed mean

In OLS, the conditional mean $E(Y \mid X)$ is modeled as a function of some regressors $X$, i.e. $$ E(Y \mid X) = X \beta. $$ Is there a regression technique that allows to model the conditional ...
30
votes
4answers
20k views

What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see ...
2
votes
0answers
231 views

How to investigate properties of the trimmed mean for a Cauchy variable?

Let $X_1,X_2, \dots,X_n$ be a sample from a population with distribution function $F(x-\theta)$, where $F$ is symmetric around $0$. The $\alpha$ trimmed mean $T_n(\alpha)=\dfrac{1}{n-2\lfloor n\alpha \...
7
votes
2answers
898 views

Given independence, is the median of a product equal to the product of the medians?

Question: Assume $X$ and $Y$ are independent random variables. Is $Median(XY) = Median(X) \cdot Median(Y)$? If so, how would one prove this? If not, what conditions would be sufficient for this ...
2
votes
1answer
371 views

Combining similarity scores

I have a list of m x n similarity score matrix, something like ...
6
votes
3answers
788 views

Mean has lower standard error than 5% trimmed mean?

I'm investigating using a trimmed mean to measure the location of various distributions. The distributions sometimes are heavily contaminated and sometimes not. Usually they follow something similar ...
2
votes
0answers
210 views

Do methods based on trimmed means require homoscedasticity?

I understand (from Wilcox' book [1]) that methods using the trimmed means are robust to distributional assumptions. Do the methods (e.g. bwtrim, from the ...
1
vote
0answers
657 views

Examining the relative efficiency of the trimmed mean

Using the following reference A survey of sampling from contaminated distributions, I am trying to investigate the relative efficiency (RE) for the mean vs the trimmed mean, given the following ...
8
votes
2answers
530 views

For what distribution is a trimmed mean the maximum likelihood estimator?

The sample mean is the maximum likelihood estimator of $\mu$ for a normal distribution $\text{Normal}(\mu,\sigma)$. The sample median is the maximum likelihood estimator of $m$ for a Laplace ...
3
votes
2answers
1k views

How to interpret output from least trimmed squares estimate and compare it to OLS?

I have to compute and compare the least squares method on a model to the least trimmed method. The LS model results were: ...
3
votes
1answer
2k views

Is it allowed to use a 5% trimmed mean for analyzing data from a creativity task (quantity of ideas)?

For my research I conducted a creativity test and measured the quantity of ideas subjects had. Some people are extreme outliers as they have a lot of ideas or only 1 or 2 ideas. Intuitively I wanted ...
1
vote
1answer
617 views

Measure of central tendency for an ex-gaussian distribution

I know there won't be a clear answer to that question but I'm really curious to know your opinion on that matter. I deal with reaction times, and finding a good measure of central tendency is ...
3
votes
2answers
7k views

Is R's trimmed means function biased?

I've been trying to understand how R's trimmed mean function works. I suspect it might be biased, but would like to get feedback here before I file a bug-report (if this is an inappropriate forum for ...
8
votes
2answers
58k views

How to calculate the truncated or trimmed mean?

How can I calculate the truncated or trimmed mean? Let's say truncated by 10%? I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?