Question

how do root finding methods such as bisection method and Newton-Rapgson method related to statistical inference?

Answer 1

Parameter estimation is an assessment of population parameter values such as mean, standard deviation, proportion, etc. Parameter estimation is based on data or samples taken from a population. Estimating the parameters of a population is one of the important things in statistical inference. There are several methods to estimate generalized linear model parameters, such as Maximum Likelihood Estimation (MLE) using a distribution approach that maximizes likelihood function. Maximum Likelihood Estimator (MLE) is a method of estimating the parameters of the data clusters following a particular distribution distribution. In this case MLE is a method applied to maximize the likelihood function and least squares method using a geometric approach by minimizing the error so that it can generate the probable parameters with maximum likelihood. In general the maximum of a function can not be solved analytically because if it is obtained implicit and nonlinear form so that it can be solved using Newton Raphson Algorithm, Fisher-Scoring Algorithm and Expectation Maximization Algorithm. Newton Raphson's algorithm is a looping procedure used to solve non-linear equations. This algorithm utilizes first order derivative vectors and second order derived matrices of maximized functions. Fisher Scoring algorithm is similar to Newton Raphson's algorithm. The difference is that fisher scoring uses the expected value of the second order derivative matrix to the parameters in the model.