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April 28, 1 Comment. I also wrote an R function to implement this method and an R script to apply this method with an example. Today, I will use apply this method to a statistical topic: minimizing the sum of absolute deviations with the median. While reading Page Section 6.
Numerical Analysis for Statisticians (Statistics and Computing)
If X is a random variable with a population mean and a population median , then. Thus, if the median minimizes , then, intuitively, it minimizes. Filed under Applied Mathematics , Data Visualization , Descriptive Statistics , Mathematics , Numerical Analysis , R programming , Statistical Computing , Statistics , Tutorials Tagged with absolute deviations , applied math , applied mathematics , math , mathematics , median , numerical analysis , numerical method , numerical methods , plot , plots , plotting , R , R programming , statistical computing , statistics , sum of absolute deviations.
April 22, 4 Comments. In an earlier post, I introduced the golden section search method — a modification of the bisection method for numerical optimization that saves computation time by using the golden ratio to set its test points.
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This post contains the R function that implements this method, the R functions that contain the 3 functions that were minimized by this method, and the R script that ran the minimization. Filed under Applied Mathematics , Data Visualization , Mathematics , Numerical Analysis , R programming , Statistical Computing , Statistics , Tutorials Tagged with applied mathematics , numerical analysis , numerical method , numerical methods , numerical optimization , optimization , R , R programming , setwd , statistical computing.
The first algorithm that I learned for root-finding in my undergraduate numerical analysis class MACM at Simon Fraser University was the bisection method. The bisection method can be easily adapted for optimizing 1-dimensional functions with a slight but intuitive modification. As there are numerous books and web sites on the bisection method, I will not dwell on it in my blog post.
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In a later post for the sake of brevity , I will use the same method to show that the minimizer of the sum of the absolute deviations from a univariate data set is the median. The EM Algorithm.
Newton's Method and Scoring. Local and Global Convergence. Advanced Optimization Topics. Concrete Hilbert Spaces.
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