1.3. Consistency of MLE
The last example de Geer (2000) presents is the consistency of maximum likelihood estimates as the last example.1 Specifically, I would like to briefly prove Hellinger consistency of MLE provided that some form of law of large numbers holds.
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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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Another semester has gone by
Another semester has gone by. It was my third semester as a graduate student and was quite fun actually, although I was frequently haunted by the fear that I (for real in this time) might fail.
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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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