Resources
This space serves as a repository for reference materials, study notes, cheat sheets, and technical guides compiled throughout my studies and research.
Posts below are arranged chronologically—spanning probability theory, machine learning, software tools, and computational notes. You can also use the Archive to browse all articles organized by tags.
Selected notes have also been compiled into standalone PDF documents:
1.2. Mean Estimation in the Binary Choice Problem
Another motivating example can be found in the estimation of mean of the binary choice model.
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1.1. Binary Choice Problem
The first chapter of Empirical Processes in M-estimation (van de Geer, 2000) devotes to introduction to the field. To be specific, it introduces two main tools that will be used throughout the textbook: the law of large numbers and the central limit theorem.
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Asymptotics is strange
It is a useful trick to “flip” the denominator into numerator when it comes to proving asymptotic properties of errors. Here’s how to do so. Consider a form
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4. Hilbert Space Theory
Objective of this chapter is to completely characterize $L^2(\mu),$ the famous Hilbert space. To achieve our goal, we will use the fact that a Hilbert space can be seen as an infinite-dimensional vector space where there exists a “orthogonal basis”. i.e. any element in the space can be decomposed into an infinite linear combination of orthogonal components. In fact, the basis decomposition yields to the main result that $L^2$ is actually isomorphic to $\ell^2.$
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3. $L^p$ Space
As we defined the Lebesgue integral and proved the basic properties, it is time to study the space of functions with finite integrals.
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