A simple example: By means of a pseudo-random generator of series, we create a Gaussian distribution (for example) of dimension 1, then we represent on a graph the normalized histogram of the distribution (Fig. 3.1). Then, we estimate the density with a Gaussian kernel and we superimpose the obtained result (the curve below) on the normalized histogram of the distribution.
Fig. 3.1 Histogram and estimated density
3.4.4 Estimator of Density and Conditional Expectation of Regression Between Two Variables
If we imagine two random variables (y, z), we can estimate the conditional density of the variable y given z. The density is written:
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