The local model for differential privacy is emerging as the reference model for practical applications of collecting and sharing sensitive information while satisfying strong privacy guarantees. In the local model, there is no trusted entity which is allowed to have each individual’s raw data as is assumed in the traditional curator model for differential privacy. Individuals’ data are usually ...

Noncentral chi-square distributions play an important role in statistics. They occur for instance as exact or limiting distributions of test statistics under alternatives. To examine the power functions of such tests we come across the problem of comparing distribution functions of noncentral chi-square variables. In this section inequalities are presented, which make such a comparison possible...

Scientists often use the Chi-square (χ) test to determine the “goodness of fit” between theoretical and experimental data. In this test, we compare observed values with theoretical or expected values. Observed values are those that the researcher obtains empirically through direct observation. The theoretical or expected values are developed on the basis of an established theory or a working hy...

We describe a lower bound for the critical value of the supremum of a ChiSquare process. This bound can be approximated using a MCQMC simulation. We compare numerically this bound with the upper bound given by Davies, only suitable for a regular Chi-Square process. In a second part, we focus a non regular Chi-Square process : the Ornstein-Uhlenbeck Chi-Square process. Recently, Rabier et al. (2...

Weighted histograms in Monte-Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiment with random events that have weights. In this paper the bin contents of a weighted histogram are considered as a sum of random variables with a random number of terms. Generalizations of the classical chi-square test for comparing ...

The Chi-square statistic is a non-parametric (distribution free) tool designed to analyze group differences when the dependent variable is measured at a nominal level. Like all non-parametric statistics, the Chi-square is robust with respect to the distribution of the data. Specifically, it does not require equality of variances among the study groups or homoscedasticity in the data. It permits...

The method of stable random projections is useful for efficiently approximating the lα distance (0 < α ≤ 2) in high dimension and it is naturally suitable for data streams. In this paper, we propose to use only the signs of the projected data and we analyze the probability of collision (i.e., when the two signs differ). Interestingly, when α = 1 (i.e., Cauchy random projections), we show that t...

The original chi-square test, often known as Pearson’s chi-square, dates from papers by Karl Pearson in the earlier 1900s. The test serves both as a ”goodnessof-fit” test, where the data are categorized along one dimension, and as a test for the more common ”contingency table”, in which categorization is across two or more dimensions. Voinov and Nikulin, this volume, discuss the controversy ove...

Knudsen and Meier applied the χ-attack to RC6. This attack is one of the most effective attacks for RC6. The χ-attack can be used for both distinguishing attacks and for key recovery attacks. Up to the present, theoretical analysis of χ-attacks, especially the relation between a distinguishing attack and a key recovery attack, has not been discussed. In this paper, we investigate the theoretica...