Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One optional observation inflates $\alpha$ by $100/\sqrt{n}$ per cent   For one-sample level $\alpha$ tests $\psi_m$ based on independent
observations $X_1,...,X_m$, we prove an asymptotic formula for the actual level
of the test rejecting if at least one of the tests $\psi_{n},...,\psi_{n+k}$
would reject. For $k=1$ and usual tests at usual levels $\alpha$, the result is
approximately summarized by the title of this paper.
  Our method of proof, relying on some second order asymptotic statistics as
developed by Pfanzagl and Wefelmeyer, might also be useful for proper
sequential analysis. A simple and elementary alternative proof is given for
$k=1$ in the special case of the Gauss test.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs