# Quantile estimation based on non-random sample points

This is my first post. I am curious to understand that what is the effect of using non-random sample to estimate the population quantile with sample quantile? Let say, I need to measure the 10th quantile of a population. Now I have non-independent sampling points from this population (samples points are auto-correlated upto lag 4). Then, is the 10th percentile of this sample will give a good statistical estimate (in terms of unbiasedness, consistency etc.) of the population 10th percentile?

Really appreciate your thought on this regards.

• If the only issue is autocorrelation, then a given sample quantile should still estimate the corresponding population quantile. – Glen_b Sep 20 '14 at 19:39
• @Glen_b thanks for your input. However still interested what is the basis of saying so? – Maural Sep 21 '14 at 8:25
• Because you're after a quantile of the marginal distribution – Glen_b Sep 21 '14 at 8:50
• Okay, let be more specific. Let I have 10,000 independent sample points. Now I calculate rolling average with length 4 which will induce autocorr in the sample. Now I calculate the 10th percentile of this new sample. Will it still estimate the population 10th percentile? – Maural Sep 21 '14 at 12:13
• The action of averaging does more than just induce autocorrelation; it also changes the variance relative to the original independent variables - so if you mean "does it give the same quantiles as on the original independent variables" the answer is no. But that's quite a different question. – Glen_b Sep 21 '14 at 12:23