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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

1 vote
1 answer
74 views

Possible error in a paper about minimal sufficient statistic and minimal sufficient $\sigma$...

According to Theorem 1 of [1], the stastistic $(X_1,\cdots,X_n)$ is minimal sufficient for the statistical model $X_1,\cdots,X_n\sim N(\theta,1)$ iid and $\theta\in\mathbb{R}$. This is false, as you c …
rfloc's user avatar
  • 649
1 vote
1 answer
151 views

Function $g:\mathbb{R}\to \mathbb{R}^n$ such that $g(\sum_{i=1}^nx_i)=(x_1,\dotsc,x_n)$ a.e

Is there a measurable function $g:\mathbb{R}\to \mathbb{R}^n$ such that $g(\sum_{i=1}^nx_i)=(x_1,\dotsc,x_n)$ a.e.? Due to the papers [1], [2], and [3] I'm obtaining a result that I think it's false. …
rfloc's user avatar
  • 649