Statistical Shrinkage

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Shrinkage in statistics has increased in popularity over the decades. Now statistical shrinkage is commonplace, explicitly or implicitly.

But when is it that we need to make use of shrinkage? At least partly it depends on signal-to-noise ratio.


Understanding False Discovery Rate

False Discovery Rate is an unintuitive name for a very intuitive statistical concept. The math involved is as elegant as possible. Still, it is not an easy concept to actually understand. Hence i thought it would be a good idea to write this short tutorial.

We reviewed this important topic in the past, here as one of three Present-day great statistical discoveries, here in the context of backtesting trading strategies, and here in the context of scientific publishing. This post target the casual reader, explaining the concept of False Discovery Rate in plain words.


Understanding K-Means Clustering


Google “K-means clustering”, and you usually you find ugly explanations and math-heavy sensational formulas*. It is my opinion that you can only understand those explanations if you don’t need them; meaning you are already familiar with the topic. Therefore, this is a more gentle introduction to K-means clustering. Here you will find out what K-Means Clustering, an algorithm, actually does. You will get only the basics, but in this particular topic, the extensions are not wildely different.


R tips and tricks – the locator function

How many times have you placed the legend in R plot to discover it is being overrun by some points or lines in the chart? Usually what comes next is a trial-and-error phase where you adjust the location, changing the arguments of the x and y coordinates, and re-drawing the plot again to check if the legend or text are now positioned such that they are fully readable.


Outliers and Loss Functions

A few words about outliers

In statistics, outliers are as thorny topic as it gets. Is it legitimate to treat the observations seen during global financial crisis as outliers? or are those simply a feature of the system, and as such are integral part of a very fat tail distribution?


Density Confidence Interval

Density estimation belongs with the literature of non-parametric statistics. Using simple bootstrapping techniques we can obtain confidence intervals (CI) for the whole density curve. Here is a quick and easy way to obtain CI’s for different risk measures (VaR, expected shortfall) and using what follows, you can answer all kind of relevant questions.


Most popular posts – 2016

Another year. Looking at my google analytics reports I can’t help but wonder how is it that I am so bad in predicting which posts would catch audience attention. Anyhow, top three for 2016 are:

On the 60/40 portfolio mix
The case for Regime-Switching GARCH
Most popular machine learning R packages

And my personal favorites:
ASA statement on p-values
Why bad trading strategies may perform well? Mathematical explanation

It is also an opportunity to say thank you, and to wish you a happy and productive 2017.

Trim your mean

The mean is arguably the most commonly used measure for central tendency, no no, don’t fall asleep! important point ahead.

We routinely compute the average as an estimate for the mean. All else constant, how much return should we expect the S&P 500 to deliver over some period? the average of past returns is a good answer. The average is the Maximum Likelihood (ML) estimate under Gaussianity. The average is a private case of least square minimization (a regression with no explanatory variables). It is a good answer. BUT:


R tips and tricks – faster loops

Insert or bind?

This is the first in a series of planned posts, sharing some R tips and tricks. I hope to cover topics which are not easily found elsewhere. This post has to do with loops in R. There are two ways to save values when looping:
1. You can predefine a vector and fill it, or
2. you can recursively bind the values.

Which one is faster?


Optimism of the Training Error Rate

We all use models. We all continuously working to improve and validate our models. Constant effort is made trying to estimate: how good our model actually is?

A general term for this estimate is error rate. Low error rate is better than high error rate, it means our model is more accurate.


Modeling Tail Behavior with EVT

Extreme Value Theory (EVT) and Heavy tails

Extreme Value Theory (EVT) is busy with understanding the behavior of the distribution, in the extremes. The extreme determine the average, not the reverse. If you understand the extreme, the average follows. But, getting the extreme right is extremely difficult. By construction, you have very few data points. By way of contradiction, if you have many data points then it is not the extreme you are dealing with.