### R and Python: Gradient Descent

December 22, 2015 |

One of the problems often dealt in Statistics is minimization of the objective function. And contrary to the linear models, there is no analytical solution for models that are nonlinear on the parameters such as logistic regression, neural networks, and nonlinear regression models (like Michaelis-Menten model). In this situation, we ... [Read more...]

### R and Python: Theory of Linear Least Squares

December 15, 2015 |

In my previous article, we talked about implementations of linear regression models in R, Python and SAS. On the theoretical sides, however, I briefly mentioned the estimation procedure for the parameter $boldsymbol{beta}$. So to help us understand how software does the estimation procedure, we'll look at the mathematics behind ... ### R, Python, and SAS: Getting Started with Linear Regression

August 16, 2015 |

Consider the linear regression model, $$y_i=f_i(boldsymbol{x}|boldsymbol{beta})+varepsilon_i,$$ where $y_i$ is the response or the dependent variable at the $i$th case, $i=1,cdots, N$ and the predictor or the independent variable is the $boldsymbol{x}$ term defined in the mean function $... [Read more...] ### Parametric Inference: Karlin-Rubin Theorem July 20, 2015 | A family of pdfs or pmfs${g(t|theta):thetainTheta}$for a univariate random variable$T$with real-valued parameter$theta$has a monotone likelihood ratio (MLR) if, for every$theta_2__theta_1$,$g(t|theta_2)/g(t|theta_1)$is a monotone (nonincreasing or nondecreasing) function of$t$on${t:g(t|... May 23, 2015 |

### R: Explore ARIMA(2, 2, 2) subclass family on Shiny

December 1, 2013 |

I've been thinking that it might be better to explore the Box-Jenkins ARIMA (Autoregressive Integrated Moving-Average) three-iterative modelling on Shiny. So here is what I got, this app is intended for ARIMA(2, 2, 2) subclass family only.The app has s... [Read more...]
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