S a is ica Sinica 35 (2025), 1-21
doi:h ps://doi.o g/10.5705/ss.202022.0279
DIFFERENTIALLY PRIVATE HYPOTHESIS TESTING
WITH THE SUBSAMPLED AND AGGREGATED
RANDOMIZED RESPONSE MECHANISM
V´ıc o Pe˜na∗and And ´es F. Ba ien os
Uni e si a Poli `ecnica de Ca alunya and Flo ida S a e Uni e si y
Abs ac : Randomized esponse is one o he oldes and mos well-known me hods
used o analyze con iden ial da a. Howe e , i s u ili y o di e en ially p i a e
hypo hesis es ing is limi ed because i canno simulaneously achie e high p i acy
le els and low ype-I e o a es. We o e come his p oblem using he subsample
and agg ega e echnique. The esul is a gene al-pu pose me hod ha can be used
o bo h equen is and Bayesian es ing. We demons a e he pe o mance o
he p oposed me hod in h ee scena ios: goodness-o - i es ing o linea eg ession
models, nonpa ame ic es ing o a loca ion pa ame e using he Wilcoxon es , and
he nonpa ame ic K uskal–Wallis es .
Key wo ds and ph ases: Bayesian hypo hesis es ing, di e en ial p i acy, hypo hesis
es ing, andomized esponse.
1. In oduc ion
In his pape , we p opose a me hod o es ing hypo heses based on con i-
den ial da a. I is concep ually simple, widely applicable, and can simul aneously
a ain high p i acy le els and low ype-I e o a es.
We wo k wi hin he di e en ial p i acy amewo k (Dwo k e al., 2006).
F om a da a p i acy pe spec i e, di e en ially p i a e algo i hms a e appealing
because hey a e obus o deanonymiza ion a acks (Dwo k and Ro h, 2014).
F om a s a is ical pe spec i e, di e en ially p i a e algo i hms a e use ul because
hey acili a e in e ences om p i a e da a.
The e is a g owing body o li e a u e on di e en ially p i a e hypo hesis
es ing. Fo example, Gaboa di e al. (2016) and Roge s and Ki e (2017) p o ide
di e en ially p i a e chi-squa ed es s, Couch e al. (2019) de elop di e en ially
p i a e e sions o nonpa ame ic es s such as he Mann–Whi ney and K uskal–
Wallis es s, and Ba ien os e al. (2019), Pe˜na and Ba ien os (2021), and Alabi
and Vadhan (2022) p opose me hods o es ing in linea eg ession models.
Ou p oposed me hod applies he subsample and agg ega e echnique (Nis-
sim, Raskhodniko a and Smi h, 2007) o andomized esponse (Wa ne , 1965).
The esul is a gene al-pu pose algo i hm ha can c ea e di e en ially p i a e
*Co esponding au ho . E-mail: ic o .pena.piza [email protected]
