Heteroscedasticity Type Error
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from Ancient Greek hetero “different” and skedasis “dispersion”) if there are sub-populations that have different variabilities from others. Here "variability" could be quantified by the variance or any other measure of heteroscedasticity definition statistical dispersion. Thus heteroscedasticity is the absence of homoscedasticity. The existence of
Heteroskedasticity Test
heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, as heteroskedasticity stata it can invalidate statistical tests of significance that assume that the modelling errors are uncorrelated and uniform—hence that their variances do not vary with the effects being modeled. For
White Test For Heteroskedasticity
instance, while the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient because the true variance and covariance are underestimated.[1][2] Similarly, in testing for differences between sub-populations using a location test, some standard tests assume that variances within groups are equal. Because heteroscedasticity concerns expectations of the second moment of the errors, its how to correct heteroskedasticity presence is referred to as misspecification of the second order.[3] Contents 1 Definition 2 Consequences 3 Detection 4 Fixes 5 Examples 6 Multivariate case 7 Notes 8 References 9 Further reading 10 External links Definition[edit] Suppose there is a sequence of random variables { Y t } t = 1 n {\displaystyle \lbrace Y_{t}\rbrace _{t=1}^{n}} and a sequence of vectors of random variables, { X t } t = 1 n {\displaystyle \lbrace X_{t}\rbrace _{t=1}^{n}} . In dealing with conditional expectations of Yt given Xt, the sequence {Yt}t=1n is said to be heteroscedastic if the conditional variance of Yt given Xt, changes witht. Some authors refer to this as conditional heteroscedasticity to emphasize the fact that it is the sequence of conditional variances that changes and not the unconditional variance. In fact, it is possible to observe conditional heteroscedasticity even when dealing with a sequence of unconditional homoscedastic random variables; however, the opposite does not hold. If the variance changes only because of changes in value of X and not because of
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Heteroskedasticity Robust Standard Errors
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Causes Of Heteroscedasticity
_ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join how to fix heteroskedasticity them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How bad can heteroscedasticity be before causing problems? up https://en.wikipedia.org/wiki/Heteroscedasticity vote 6 down vote favorite I have two questions about heteroscedasticity in multiple regressions. According to my trusty textbook (Using Multivariate Statistics 2007, p.127), it says that deviations from heteroscedasticity only reduce that statistical power of a test, rather than inflating the type I error rate (is this true?) I wanted to know if there were any guidelines about how to judge effect sizes for heteroscadisticity and how much is a bad effect size for it to matter (with N=187). http://stats.stackexchange.com/questions/133272/how-bad-can-heteroscedasticity-be-before-causing-problems Because I use two categorical variables, luckily my residual/predicted plot is in two distinct clumps that I can analyse (see below): regression heteroscedasticity assumptions type-i-errors type-ii-errors share|improve this question edited Jan 13 '15 at 19:18 gung 74.2k19160309 asked Jan 13 '15 at 19:05 user3084100 669 1 In real life problems heteroscedasticity could be the symptom of a more serious misspecification issue. For instance, it may indicate that you should be using unit root process instead of trend stationary. –Aksakal Jan 13 '15 at 19:24 I don't have time to post this as an answer but point 1 is not necessarily true. Try this R code: x <- c(rep(0, 9), 1); y <- c(rnorm(mean=0, n=9, sd=1), rnorm(mean=0, n=1, sd=100)); summary(lm(y~x)). The conditional mean of y is 0 everywhere but the variance is much higher when x=1. I only put one point at x=1, you can see the results! –Silverfish Jan 13 '15 at 19:37 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote It is true that heteroscedasticity reduce your power (see: Efficiency of beta estimates with heteroscedasticity), but it can also inflate type I errors. Consider the following simulation (coded in R): set.seed(1044) # this makes the example exactly reproducible b0 = 10 # these are the true values of the intercept b1 = 0 # & the slope x = rep(c(0, 2, 4), each=10) # these are
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