We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism [War65, KLN08] and the newer (non-symmetric) mechanisms [BS15, BNST17]. First, we study the general framework of mapping each user’s type into a signal and show that the problem of finding the maximumlikelihood distribution over the signals is ...

T he process of drawing conclusions about an entire population on the basis of the information contained in a random sample drawn from that population is known as statistical inference. Methods of statistical inference fall into 2 general categories: estimation and hypothesis testing. With estimation, our goal is to describe or estimate some characteristic of a population of interest, such as t...

In this paper we study fuzzy multiobjective optimization problems defined for $n$ variables.  Based on a new $p$-dimensional fuzzy stationary-point definition,  necessary  efficiency conditions are obtained.  And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.

companies' continuity, because all companies have some relations with the society;Therefore, the society provides long-term survival of the company.In this way, companies in addition to economic responsibility, must take responsibilityof social issues. Therefore, with respect to corporate social responsibility andits revelations, the current paper examines the relationship between social respon...

Falsification may demarcate science from non-science as the rational way to test the truth of hypotheses. But experimental evidence from studies of reasoning shows that people often find falsification difficult. We suggest that domain expertise may facilitate falsification. We consider new experimental data about chess experts’ hypothesis testing. The results show that chess masters were readil...

Statistical Hypothesis • Null hypothesis (H0): Hypothesis of no difference or no relation (or not guilty) and often has =, ≥, or ≤ notation in the mathematical statement of the hypothesis. A theory about the values of one (or more) population parameter(s). The theory generally represents the status quo, which we accept until it is proven false. Example: H0: μ = 98.6F (average body temperature i...

1 From the Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, Mass (K.H.Z., J.R.F., S.G.S., C.M.C.T.); and Department of Health Care Policy, Harvard Medical School, 180 Longwood Ave, Boston, MA 02115 (K.H.Z.). Received September 10, 2001; revision requested November 8; revision received December 12; accepted December 19. Supported in part by Public Health Ser...

Suppose we are using a pH meter to test acidity/alkalinity of a solution used in a manufacturing process. The pH of pure water is 7.00. For samples in the pH range from about 5 to 9 the meter gives normally distributed readings with • μ equal to the true pH of the sample and • standard deviation σ = 0.20. The meter is tested each morning to make sure it is operating properly: n = 4 samples of p...

In statistical applications, such as a comparison of two items, it is useful to know whether one item is equivalent to another. Similarly it is often desirable to know whether one item can act as a substitute for another. Applications of the concept of equivalence include blend and flavor modifications of products, substitution of generic drugs for brand-name drugs, modifications of products in...