2 3 Se p 20 09 A simpler proof of the negative association property for absolute values of measures tied to generalized Orlicz balls ∗ †
نویسنده
چکیده
Negative association for a family of random variables (Xi) means that for any coordinate–wise increasing functions f, g we have Ef(Xi1 , . . . , Xik )g(Xj1 , . . . , Xjl ) ≤ Ef(Xi1 , . . . , Xik )Eg(Xj1 , . . . , Xjl ) for any disjoint sets of indices (im), (jn). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics, and brought to convex geometry in 2005 to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of negative association of absolute values for a wide class of measures tied to generalized Orlicz balls, including the uniform measures on generalized Orlicz balls.
منابع مشابه
The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball
Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for generalized Orlicz balls. This allows us to give a strong concentration property, along with a few moment comparison inequalities. Also, the theory of negatively as...
متن کاملThe square negative correlation property for generalized Orlicz balls
Recently Antilla, Ball and Perissinaki proved that the squares of coordinate functions in ln p are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on Rn. From this, the concentration of the Euclidean norm and a form of the Central Limit Theorem for the generalized Orlicz balls is deduced. Also, a counterexample for the square negative correlation hyp...
متن کاملA New Proof of FDR Control Based on Forward Filtration
For multiple testing problems, Benjamini and Hochberg (1995) proposed the false discovery rate (FDR) as an alternative to the family-wise error rate (FWER). Since then, researchers have provided many proofs to control the FDR under different assumptions. Storey et al. (2004) showed that the rejection threshold of a BH step-up procedure is a stopping time with respect to the reverse filtration g...
متن کاملWEAR RATE PREDICTION OF GRINDING MEDIA USING BPNN AND MLR MODELS IN GRINDING OF SULPHIDE ORES
Nowadays steel balls wear is a major problem in mineral processing industries and forms a significant part of the grinding cost. Different factors are effective on balls wear. It is needed to find models which are capable to estimate wear rate from these factors. In this paper a back propagation neural network (BPNN) and multiple linear regression (MLR) method have been used to predict wear rat...
متن کاملAnalysis of a Problem Using Various Visions
In this paper an applied problem, where the response of interest is the number of success in a specific experiment, is considered and by various visions is studied. The effects of outlier values of response on results of a regression analysis are so important to be studied. For this reason, using diagnostic methods, outlier response values are recognized. It is shown that use of arc-sine ...
متن کامل