Hypothesis testing for densities and high-dimensional multinomials: Sharp local minimax rates
密度与高维多项分布的假设检验:精确局部极小极大速率
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or unbounded number of categories. In the continuous case, we consider testing a Hölder density with exponent $0