# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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### Why doesn't increasing N guarantee the sample mean will get closer to the population mean?

When sampling from a population, the sample mean will always be closer to the population mean as the sample size increases. Why is this statement wrong? My explanation is that as sample size ...
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### Mathematical basis for conditional probability

In order to get more fundamental in my understanding of probability I watched mathematicalmonk's lectures involving $\sigma$-algebras etc. - good. One of my main concerns was to better understand the ...
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### Statistical properties of parameters estimated by method of Lagrange multipliers in R

I have time series data that can be fitted by a constrained non-linear function (non-linear in the parameters to be estimated). I'd like to use the method of Lagrange Multipliers (link), specifically ...
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### statistical derivation of Pearson correlation of two variables obtained from regression model

I have asked a stat question on math.SE which now I believe should be here. However, I repeat it here. As a newcomer, I would appreciate it if you could excuse me for any mistakes or repeating the ...
207 views

### Random forest like procedure for regression or other statistical models

I'm wondering if there exist methods similar to one used in random forest algorithm - I mean taking simultaneously bootstrap sample and random subset of features, then building statistisal model. Have ...
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### How to combine 3 random variables?

I have a homework assignment that is giving me a hard time on the statistics. Lets say you have 3 stocks, all with n expected return (mean) $\mu = 8\%$, a risk (standard deviation) $\sigma = 16\%$ and ...
I am trying to show that the central moment of a symmetric distribution: $${\bf f}_x{\bf (a+x)} = {\bf f}_x{\bf(a-x)}$$ is zero for odd numbers. So for instance the third central moment {\bf E[(...