How to insert math symbols & formulas by Latex on Blogger

In order to insert math symbols & formulas by Latex on Blogger, just drop in

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js">
MathJax.Hub.Config({
 extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
 jax: ["input/TeX", "output/HTML-CSS"],
 tex2jax: {
     inlineMath: [ ['$','$'], ["\\(","\\)"] ],
     displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
 },
 "HTML-CSS": { availableFonts: ["TeX"] }
});
</script>

after the header (<head>) in the Blogger template.

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Weighted Percentile in Python Pandas

Unfortunately, there is no weighted built-in functions in Python. If we want to get some weighted percentiles by Python, one possible method is to extend the list of data, letting the values of weight as the numbers of elements, which is discussed in a Stack Overflow poster . For example, if we have a data like, score weight 5 2 4 3 2 4 8 1 we firstly extend the list of scores to {5, 5, 4, 4, 4, 2, 2, 2, 2, 8}, and then find the percentiles such as 10% or 50% percentile. The limitations of this method are, (1) weight must be integers; (2) values of weight cannot be very large. What if we want to calculate the weighted percentiles of a large dataset with very large non-integer weights? In this article, I want to show you an alternative method, under Python pandas. step1: given percentile q, (0<=q<=1), calculate p = q * sum of weights; step2: sort the data according the column we want to calculate the weighted percentile thereof;

Rcpp Example: Partition Based Selection Algorithm

In this post, I'm going to take a Rcpp example that call a C++ function to find kth smallest element from an array. A partition-based selection algorithm could be used for implementation. A most basic partition-based selection algorithm, quickselect , is able to achieve linear performance to find the kth element in an unordered list. Quickselect is a variant of quicksort , both of which choose a pivot and then partitions the data by it. The procedure of quickselect is to firstly move all elements smaller than the pivot to the left and what greater than the pivot the the right by exchanging the location of them, given a pivot such as the last element in the list; and then to move the elements in the left or right sublist again according to a new pivot until getting exact kth elements. The difference from quicksort is that quickselect only need to recurses on one side where the desired kth element is, instead of recursing on both sides of the partition which is what quicksort

Trend Removal Using the Hodrick-Prescott (HP) Filter

Hodrick-Prescott filter (see Hodrick and Prescott (1997)) is a popular tool in macroeconomics for fitting smooth trend to time series. In SAS, we can use PROC UCM to realize the HP filter. The dataset considered in this example consists of quarterly real GDP for the United States from 1947-2016 (b illions of chained 2009 dollars , seasonally adjusted annual rate ). The data can be download from this link https://fred.stlouisfed.org/series/GDPC1 %macro hp(input= ,date= ,int= ,var= ,par= ,out= ); proc ucm data=&input; id &date interval=∫ model &var; irregular plot=smooth; level var= 0 noest plot=smooth; slope var=&par noest; estimate PROFILE; forecast plot=(decomp) outfor=&out; run; %mend ; % hp (input=gdp,date=year,int=qtr,var=gdp,par= 0.000625 ,out=result); I use SAS MACROS to define a function for HP filter. "input" is the data file you use, "date" is the variable for time, "int&qu

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