Martin's Sandbox

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How was it...Hlelo Wrold

iltaic

blod

itlaic & blod

The model:

Gvien are $\vec S_{\it exp}, \vec S_{\it th} = \sum_{i=1}^{n}\alpha_i\vec s_i + \sigma \mathcal{N} (0,1)$ . Find $n, \vec s_i, \alpha_i$ , such that $d(\vec S_{\it exp}, \sum\alpha_i\vec s_i) = min$ , where $d$ is some measure function blah blah.

Let $\chi^2_N = \frac{1}{N}\sum_{i=1}^N\frac{(S_i - (s_i+\sigma\mathcal{N}(0,1))^2}{\sigma^2}, N>>1$ .

If $s_i = S_i, \forall i$ then $\chi^2_N \sim \mathcal{N}(1,\frac{2}{N})$ . The converse is not necessarily true. Optimally, the test should be used to reject the null hypothesis.