July 2nd, 2015, 12:01 pm
What is the spurious input?The standard error is usually quoted as a root mean square error, i.e.[$]\sqrt{E |X_M - \mu|^2} \leq \frac{std(X)}{\sqrt{M}}[$]But this is an average error. For a given realisation of [$]X_M[$] you don't know a priori how close to [$]\mu[$] it actually is, you only know that ON AVERAGE it is close. I was just telling you how to get a bound on the probability that [$]X_M[$] is actually close to [$]\mu[$].