Testing Unbiasedness of Testing a Sequence of Tests

The paper investigates testing whether a sequence of independent binary test outcomes matches a prediction. Building on the results of [1], we explore several composite-hypothesis tests (GLR, Rao, Wald, etc.), but find that no unbiased test exists with only one scan. We also show that, with multiple looks, unbiased testing indeed does become possible.

[1]  Stephen E. Fienberg,et al.  Testing Statistical Hypotheses , 2005 .

[2]  H. Vincent Poor,et al.  An Introduction to Signal Detection and Estimation , 1994, Springer Texts in Electrical Engineering.

[3]  Peter Willett,et al.  The Importance of Being Earnest: Social Sensing With Unknown Agent Quality , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[4]  Stefan Aachen,et al.  Signal Detection In Non Gaussian Noise , 2016 .

[5]  J. G. Gander,et al.  An introduction to signal detection and estimation , 1990 .

[6]  Peter K. Willett,et al.  Algorithms and Fundamental Limits for Unlabeled Detection Using Types , 2018, IEEE Transactions on Signal Processing.

[7]  Stefano Marano,et al.  Shuffled Bits in the Low-Detectability Regime , 2019, 2019 27th European Signal Processing Conference (EUSIPCO).

[8]  Charu C. Aggarwal,et al.  On Credibility Estimation Tradeoffs in Assured Social Sensing , 2013, IEEE Journal on Selected Areas in Communications.

[9]  Pierluigi Salvo Rossi,et al.  A Systematic Framework for Composite Hypothesis Testing of Independent Bernoulli Trials , 2015, IEEE Signal Processing Letters.