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POR: running standard deviations
 

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  1. POR: running standard deviations
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    <p>I need to compute the "running" standard deviations of a vector of means, computing them as if the sample size is increasing. In other words, I need to compute the sd of mean_y[1], of mean_y[1] and mean_y[2], of mean_y[1], mean_y[2], mean_y[3] and so on,</p> <p>where:</p> <pre><code>y &lt;- rnorm(10000, mean=5, sd=2) i &lt;- seq(1 : length(y)) mean_y &lt;- cumsum(y)/i </code></pre> <p>Trying to apply the same criterion (hence, not explicitly using a loop), I produced the following code for the standard deviations of the vector of running means:</p> <pre><code>se &lt;- sqrt(1/i^2*cumsum(y^2) - 1/i*mean_y^2) </code></pre> <p>This beacuse, var(mean(x)) = 1/n*var(x). To me, the code seems ok. But when I plot the runnning means with their confidence intervals against i (the increasing sample size), the 95% bands perfectly coincide with the means!</p> <p>The code is:</p> <pre><code>error &lt;- qnorm(0.975)*se/sqrt(i) lower &lt;- mean_y - error upper &lt;- mean_y + error # plotting means and ci's against sample size (= up to 10000) plot(x=i, y=mean_y, xlab="Number of iterations (sample size)", ylab="E[y] estimates and 95% CI's", cex=0.4, ylim=c(4.6, 5.4)) lines(lower, col="gold") lines(upper, col="gold") </code></pre> <p>The rationale is to produce a graph showing the convergence of the estimator "mean_y" as the sample size keeps increasing.</p> <p>Can anyone help me? Probably there is some kind of basic error, either in the <code>se</code> formula or in <code>lower</code> and <code>upper</code>. Thanks!! Stefano </p>
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    1. USStezzo
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      1. POR: running standard deviations
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      1. VTUpMod
    1. COI'd just go with `se <- sapply(1:length(y),function(x) sd(y[1:x]))` or something close to that
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      1. POR: running standard deviations
      1. USCarl Witthoft
    2. COI think you are diving by `i` once too often. You divide through in `se` then again by the `sqrt(i)` in the `error` formula
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      1. POR: running standard deviations
      1. UScsgillespie
 

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