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What are some recommended Graduate-Level Probability and/or Statistics textbooks for an incoming Econ PhD Student?

Here are a couple of grad-level books that cover probability and stats at a high level of rigor as a foundation for econometrics: The first is Bierens, Herman J.. Introduction to the Mathematical and ...
4 votes

Markov Chains with Changing Number of States

This is essentially just a regular Markov chain (under some simplifying assumptions) At present your question is a little ill-posed, since you appear to conflate the value of the exogenous variable $\...
Ben's user avatar
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4 votes

Markov Chains with Changing Number of States

I suppose this process I described in my question no longer follows the memoryless property. The memoryless property means that the transition to the next state is independent from the past, ...
Sextus Empiricus's user avatar
2 votes

Nice real datasets for visually illustrating concepts

The gamair package contains many datasets used explicitly for modeling generalized additive models (GAMs) and would make for good examples for nonlinear regression ...
2 votes

Nice real datasets for visually illustrating concepts

Here is a an example of nonlinear regression. (It has heteroscedasticity as an added bonus!). This Motorcycle dataset is popular in the computer experiments community as an illustrative example. It ...
0 votes

References to learn « Real and Functional Analysis for Statisticians »

Jun Shao's book and Keener's book are both proof based, and would require background in analysis. My favorite text for basic analysis is "Introduction to Analysis in One Variable" by M. ...
Kakashi's user avatar
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6 votes

References to learn « Real and Functional Analysis for Statisticians »

To study books like that of Shao's, Keener's or some other books of similar breed, you need to have a robust concept of not only real analysis but measure theory, general topology and functional ...
User1865345's user avatar
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0 votes

Alternatives to Vector Autoregression

I'm a bit late to this party but depending on what you're trying to do, an OLS with time series errors model, or Vector Error Correction Models (VECMs) could work as an alternative to VAR if you're ...
Angela Helvin's user avatar
3 votes
Accepted

Normal approximation for posterior distribution

The normal distribution wouldn't really make sense in this case because the normal distribution is a continuous distribution and your target posterior distribution is a discrete distribution over the ...
Andrew Hollis's user avatar

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