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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Define a conditional median of Y given X = x to be any median of the conditional distribution of Y given X = x. Suppose that we will get to observe X and then we will need to predict Y. Suppose that we wish to choose our prediction d(X) so as to minimize mean absolute error (MAE), E(|Y − d(X)|). Prove that d(x) should be chosen to be a conditional median of Y given X = x. You can use the fact that for a univariate random variable MAE is minimized at the median, m.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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