Blog Archives

R, Python, and SAS: Getting Started with Linear Regression

August 16, 2015
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R, Python, and SAS: Getting Started with Linear Regression

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 $f_i(boldsymbol{x}|boldsymbol{beta})$. For simplicity, consider the following simple linear regression (SLR) model, $$ y_i=beta_0+beta_1x_i+varepsilon_i. $$ To obtain the (best) estimate...

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Parametric Inference: Karlin-Rubin Theorem

July 20, 2015
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Parametric Inference: Karlin-Rubin Theorem

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 ${t:g(t|theta_1)>0;text{or};g(t|theta_2)>0}$. Note that $c/0$ is defined as $infty$ if $0< c$. Consider testing $H_0:thetaleq theta_0$ versus $H_1:theta>theta_0$. Suppose that $T$...

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Parametric Inference: Likelihood Ratio Test Problem 2

May 23, 2015
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Parametric Inference: Likelihood Ratio Test Problem 2

More on Likelihood Ratio Test, the following problem is originally from Casella and Berger (2001), exercise 8.12.ProblemFor samples of size $n=1,4,16,64,100$ from a normal population with mean $mu$ and known variance $sigma^2$, plot the power function of the following LRTs (Likelihood Ratio Tests). Take $alpha = .05$. $H_0:muleq 0$ versus $H_1:mu>0$$H_0:mu=0$ versus $H_1:muneq 0$SolutionThe LRT statistic...

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Python and R: Basic Sampling Problem

April 16, 2015
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In this post, I would like to share a simple problem about sampling analysis. And I will demonstrate how to solve this using Python and R. The first two problems are originally from Sampling: Design and Analysis book by Sharon Lohr.ProblemsLet $N=6$ and $n=3$. For purposes of studying sampling distributions, assume that all population values are known.

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R: How to Layout and Design an Infographic

February 26, 2015
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R: How to Layout and Design an Infographic

As promised from my recent article, here's my tutorial on how to layout and design an infographic in R. This article will serve as a template for more infographic design that I plan to share on future posts. Hence, we will go through the following sect...

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Philippine Infographic: Recapitulation on Incidents Involving Motorcycle Riding in Tandem Criminals for 2011-2013

February 18, 2015
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Philippine Infographic: Recapitulation on Incidents Involving Motorcycle Riding in Tandem Criminals for 2011-2013

The Philippine government has launched Open Data Philippines (data.gov.ph) last year, January 16, 2014. Accordingly, the data.gov.ph aims to make national government data searchable, accessible, and useful, with the help of the different agencies of go...

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Canonical Correlation Analysis on Imaging

January 5, 2015
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Canonical Correlation Analysis on Imaging

In imaging, we deal with multivariate data, like in array form with several spectral bands. And trying to come up with interpretation across correlations of its dimensions is very challenging, if not impossible. For example let's recall the number of s...

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Principal Component Analysis on Imaging

December 25, 2014
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Principal Component Analysis on Imaging

Ever wonder what's the mathematics behind face recognition on most gadgets like digital camera and smartphones? Well for most part it has something to do with statistics. One statistical tool that is capable of doing such feature is the Principal Component Analysis (PCA). In this post, however, we will not do (sorry to disappoint you) face recognition as...

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ALUES: Agricultural Land Use Evaluation System, R package

October 26, 2014
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Authors:Arnold R. Salvacion                                                                       [email protected] Analysis and Visualization using R (blog)                                          Al-Ahmadgaid B. Asaad (maintainer)[email protected] Land Use Evaluation System (ALUES) is an R package that evaluates land suitability for different crop production. The package is based on the Food and Agriculture Organization (FAO) and the International Rice Research Institute (IRRI) methodology for land evaluation. Development...

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R: k-Means Clustering on an Image

September 12, 2014
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R: k-Means Clustering on an Image

Enough with the theory we recently published, let's take a break and have fun on the application of Statistics used in Data Mining and Machine Learning, the k-Means Clustering.k-means clustering is a method of vector quantization, originally from signa...

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