We study the analysis of a joint association between a genetic marker with both binary (case-control) and quantitative (continuous) traits, where the quantitative trait values are only available for the cases due to data sharing and outcome-dependent sampling. Data sharing becomes common in genetic association studies, and the outcome-dependent sampling is the consequence of data sharing, under...

Let Yi = f(xi) + Ei (1 ≤ i ≤ n) with given covariates x1 < x2 < · · · < xn, an unknown regression function f and independent random errors Ei with median zero. It is shown how to apply several linear rank test statistics simultaneously in order to test monotonicity of f in various regions and to identify its local extrema.

Introduction: Borago officinalis flower (borage) is a known sedative in herbal medicine the aim of the present study was to evaluate the antinociceptive effect of borage hydroalcoholic extract in formalin test male rats. Methods: Fifty-six adult male albino Wistar rats were randomly divided into seven groups: Control groups of A (intact), B (saline), and C (Positive control) plus test grou...

A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f(x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the ...

Partial F tests play a central role in model selections in multiple linear regression models. This paper studies the partial F tests from the view point of simultaneous confidence bands. It first shows that there is a simultaneous confidence band associated naturally with a partial F test. This confidence band provides more information than the partial F test and the partial F test can be regar...

Today we will finish developing a tester for dictator functions and then explore connections of this test (and the linearity test discussed last lecture) with error correcting codes and probabilisti-cally checkable proofs. In the last lecture, we introduced and analyzed a local tester for linearity and began to reverse engineer how it could be modified to yield a test for dictatorships. Recall ...

In this article, we have proved the correctness of the Public-Key Cryptography and the Pepin’s Test for the Primality of Fermat Numbers (F(n) = 22 n + 1). It is a very important result in the IDEA Cryptography that F(4) is a prime number. At first, we prepared some useful theorems. Then, we proved the correctness of the Public-Key Cryptography. Next, we defined the Order’s function and proved s...