Improvement on Chi-Squared Approximation by Monotone Transformation

Notes on the chi-squared distribution

CHI-Squared Test of Independence

Chi-square (X) test is a nonparametric statistical analyzing method often used in experimental work where the data consist in frequencies or ‘counts’ – for example the number of boys and girls in a class having their tonsils out – as distinct from quantitative data obtained from measurement of continuous variables such as temperature, height, and so on. The most common use of the test is to ass...

Information Divergence is more chi squared distributed than the chi squared statistics

For testing goodness of fit it is very popular to use either the χ-statistic or G-statistics (information divergence). Asymptotically both are χ-distributed so an obvious question is which of the two statistics that has a distribution that is closest to the χ-distribution. Surprisingly, when there is only one degree of freedom it seems like the distribution of information divergence is much bet...

On 3-monotone approximation by piecewise polynomials

Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...

Differentially Private Chi-squared Test by Unit Circle Mechanism

We describe Algorithm 2 in detail. Algorithm 2 takes as input the sample set S, the query sequence F , the sensitivity of query ∆, the threshold τ , and the stop parameter s. Algorithm 2 outputs the result of each comparison with the threshold. In Algorithm 2, each noisy query output is compred with a noisy threshold at line 4 and outputs the result of comparison. Let ⊤ mean that fk(S) > τ . Al...