A Note on Quantile Coupling Inequalities and Their Applications
نویسنده
چکیده
A relationship between the large deviation and quantile coupling is studied. We apply this relationship to the coupling of the sum of n i.i.d. symmetric random variables with a normal random variable, improving the classical quantile coupling inequalities (the key part in the celebrated KMT constructions) with a rate 1= p n for random variables with continuous distributions, or the same rate modulo constants for the general case. Applications to the asymptotic equivalence theory and nonparametric function estimation are discussed.
منابع مشابه
Quantile coupling inequalities and their applications
This is partly an expository paper. We prove and highlight a quantile inequality that is implicit in the fundamental paper by Komlós, Major, and Tusnády [31] on Brownian motion strong approximations to partial sums of independent and identically distributed random variables. We also derive a number of refinements of this inequality, which hold when more assumptions are added. A number of exampl...
متن کاملA note on the Young type inequalities
In this paper, we present some refinements of the famous Young type inequality. As application of our result, we obtain some matrix inequalities for the Hilbert-Schmidt norm and the trace norm. The results obtained in this paper can be viewed as refinement of the derived results by H. Kai [Young type inequalities for matrices, J. Ea...
متن کاملA Note on the Smooth Estimator of the Quantile Function with Left-Truncated Data
This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.
متن کاملSynchronization analysis of complex dynamical networks with hybrid coupling with application to Chua’s circuit
Complex dynamic networks have been considered by researchers for their applications in modeling and analyzing many engineering issues. These networks are composed of interconnected nodes and exhibit complex behaviors that are resulted from interactions between these nodes. Synchronization, which is the concept of coordinated behavior between nodes, is the most interested behavior in these netwo...
متن کاملA note on inequalities for Tsallis relative operator entropy
In this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy, {em Math. Inequal. Appl.} {18} (2015), no. 2, 401--406]. Meanwhile, we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...
متن کامل