Large deviations in testing Jacobi model

TL;DR: In this paper, a new strategy to establish large deviations and concentration inequalities for the maximum likelihood estimator of the drift parameter of the Ornstein-Uhlenbeck process without tears is proposed.

TL;DR: In this paper, deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model were studied. But the deviation inequalities were not applied to the Laplace integrals of the functionals.

TL;DR: In this paper, the authors studied hypothesis testing in time inhomogeneous diffusion processes and obtained the negative regions and decay rates of the error probabilities with the help of large and moderate deviations for the log-likelihood ratio process.

TL;DR: In this paper, the authors studied the sharp large deviations for the log-likelihood ratio of an α-Brownian bridge, and the full expansion of the tail probability was obtained by using a change of measure.

TL;DR: The testing of binary hypotheses is developed from an information-theoretic point of view, and the asymptotic performance of optimum hypothesis testers is developed in exact analogy to the ascyptoticperformance of optimum channel codes.

TL;DR: In this paper, the authors obtained the explicit form of fine large deviation theorems for the log-likelihood ratio in testing models with fractional Ornstein-Uhlenbeck processes with Hurst parameter bigger than half and obtains the explicit rates of decrease of the error probabilities of Neyman-Pearson, Bayes and minimax tests.

TL;DR: In this article, the authors considered a signal detection problem for continuous-time stationary diffusion processes and showed that the error probability of the second kind of signal detection tends to zero or one exponentially fast, depending on the fixed exponent of the diffusion process.

TL;DR: In this paper, the authors obtained exact large deviation rates for the log-likelihood ratio in testing models with observed Ornstein-Uhlenbeck processes and gave explicit rates of decrease for the error probabilities of Neyman-Pearson, Bayes, and minimax tests.