Parametric vs non-Parametric Linear Models (LM)

 a  b

Histogram: LM estimates of Intercepts

Histogram: LM estimates of Gradient

 c  d

QQ Plot: LM estimates of Intercepts

QQ Plot: LM estimates of Gradient

Figure 1: Gradient  appears to follow a normal distribution more than intercept .

When do we use a parametric model, and when do we use a non-parametric one? In the above example, “Intercept” is one random variable, and “Gradient” is another. I will show you why “Intercept” is better modeled by a non-parametric model, and “Gradient” is better modeled by a parametric one.

In Figure 1, histograms and QQ plots of “Intercept”  and “Gradient”  show that the latter appears to follow a normal distribution whereas the former does not. As such, a parametric (normal) distribution would not be appropriate for modelling “Intercept”. This leads us to believe that a non-parametric distribution is a better method for estimating “Intercept”.

However, a parametric (normal) distribution might be appropriate for modelling “Gradient”, which appears to follow a normal distribution, according to both its histogram and QQ plot.

Abbas Keshvani

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