Goodness-of-Fit Testing for Hölder Continuous Densities Under Local Differential Privacy

We address the problem of goodness-of-fit testing for Hölder continuous densities under local differential privacy constraints. study minimax separation rates when only non-interactive mechanisms are allowed to be used and both sequentially interactive can privatisation. propose associated procedures whose analysis enables us obtain upper bounds on rates. These results complemented with lower bounds. By comparing these bounds, we show that proposed tests optimal up at most a logarithmic factor several choices $$f_0$$ including from uniform, normal, Beta, Cauchy, Pareto, exponential distributions. In particular, observe deteriorated in private setting compared non-private one. Moreover, improve upon obtained considering mechanisms.