# Standard error of a statistic

the standard error of a standard deviation is given as : s/n^(1/2). Would the standard error of kurtosis and skewness follow the same idea? For example, se of kurtosis = kurtosis/n^(1/2)?

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Are you asking about the standard deviation of moment estimators? For a estimator of the mean, i.e. $$\hat{m} = \frac{1}{n} \sum_{k=1}^n X_k$$ the variance is $$\mathbb{Var}(\hat{m}) = \mathbb{E}(\hat{m}^2) - \mathbb{E}(\hat{m})^2 = \frac{\mathbb{Var}(X)}{n}$$ which is what you claimed first. So, rephrasing the question, are you asking for variances of the skewness and kurtosis estimators? If so, you need to precise which estimators you have in mind, biased/unbiased, based on symmetric polynomials of the sample data, or on quantiles, etc. – Sasha Nov 3 '12 at 17:02
well, I already have a given data. I am trying to compute the standard error of the sample kurtosis of the data in R. So, I was wondering if the formula for Se = Kurtosis/n^(1/2) – Josh Nov 3 '12 at 17:13