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We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We show that two classes of Maximum Mean Discrepancy (MMD) based tests attain this optimality on Rd, while the quadratictime Kernel Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate under a relaxed level constraint. Under the same performance metric, we proceed to show that the quadratic-time MMD based two-sample tests are also optimal for general two-sample problems, provided that kernels are bounded continuous and characteristic. Key to our approach are Sanov’s theorem from large deviation theory and the weak metrizable properties of the MMD and KSD. 

Abstract We explore the decay of bound neutrons in the JUNO liquid scintillator detector into invisible particles (e.g.,$$n\rightarrow 3 \nu $$ $n\to 3\nu$or$$nn \rightarrow 2 \nu $$ $nn\to 2\nu$), which do not produce an observable signal. The invisible decay includes two decay modes:$$ n \rightarrow { inv} $$ $n\to \mathrm{inv}$and$$ nn \rightarrow { inv} $$ $nn\to \mathrm{inv}$. The invisible decays ofs-shell neutrons in$$^{12}\textrm{C}$$ $_{}^{12}\text{C}$will leave a highly excited residual nucleus. Subsequently, some de-excitation modes of the excited residual nuclei can produce a time- and space-correlated triple coincidence signal in the JUNO detector. Based on a full Monte Carlo simulation informed with the latest available data, we estimate all backgrounds, including inverse beta decay events of the reactor antineutrino$${\bar{\nu }}_e$$ ${\overline{\nu }}_e$, natural radioactivity, cosmogenic isotopes and neutral current interactions of atmospheric neutrinos. Pulse shape discrimination and multivariate analysis techniques are employed to further suppress backgrounds. With two years of exposure, JUNO is expected to give an order of magnitude improvement compared to the current best limits. After 10 years of data taking, the JUNO expected sensitivities at a 90% confidence level are$$\tau /B( n \rightarrow { inv} ) > 5.0 \times 10^{31} \, \textrm{years}$$ $\tau /B(n\to \mathrm{inv})>5.0\times {10}^{31}\text{years}$and$$\tau /B( nn \rightarrow { inv} ) > 1.4 \times 10^{32} \, \textrm{years}$$ $\tau /B(nn\to \mathrm{inv})>1.4\times {10}^{32}\text{years}$.