MEAN SQUARE ERROR DERIVATION

• In speech recognition, we prefer to use a statistical approach to estimating the derivative. Why?
  
  
• This technique uses a statistical method known as linear regression. In this approach, we choose the regression coefficients to minimize the mean squared error:
• The solution to this equation is well-known (in DSP literature, this is known as linear prediction), and is found by differentiating the error equation with respect to the regression coefficients, setting the derivative to zero, and solving for the regression coefficients. This results in the following equations:
• This equation is fairly general. Note that if the input data have an average value of zero, the resulting equations are even simpler.