Search results
Results from the WOW.Com Content Network
Square root biased sampling is a sampling method proposed by William H. Press, a computer scientist and computational biologist, for use in airport screenings. It is the mathematically optimal compromise between simple random sampling and strong profiling that most quickly finds a rare malfeasor, given fixed screening resources. [1] [2]
The standard deviations will then be the square roots of the respective variances. Since the square root introduces bias, the terminology "uncorrected" and "corrected" is preferred for the standard deviation estimators: s n is the uncorrected sample standard deviation (i.e., without Bessel's correction)
Since the square root is a strictly concave function, it follows from Jensen's inequality that the square root of the sample variance is an underestimate. The use of n − 1 instead of n in the formula for the sample variance is known as Bessel's correction , which corrects the bias in the estimation of the population variance, and some, but ...
The use of the term n − 1 is called Bessel's correction, and it is also used in sample covariance and the sample standard deviation (the square root of variance). The square root is a concave function and thus introduces negative bias (by Jensen's inequality ), which depends on the distribution, and thus the corrected sample standard ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
Here taking the square root introduces further downward bias, by Jensen's inequality, due to the square root's being a concave function. The bias in the variance is easily corrected, but the bias from the square root is more difficult to correct, and depends on the distribution in question.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
If y n < f(0), then the initial estimate x 1 was too high. Given this, use a root-finding algorithm (such as the bisection method) to find the value x 1 which produces y n−1 as close to f(0) as possible. Alternatively, look for the value which makes the area of the topmost layer, x n−1 (f(0) − y n−1), as close to the desired value A as