Introduction to mathematical statistics
by Robert V. Hogg · first published 1959
43% recommend57% neutral
The fifth edition of this text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference.
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…the first year of my PhD program in Economics. But it's probably worth starting with a basic probability and statistics book, preferably one that's pretty mathematical. I've used Hogg McKean and Craig's Introduction to Mathematical Statistics and it's really good.
on “For Today’s Graduate, Just One Word: Statistics” ↗If you're looking for just mathematical statistics, I liked Hogg McKean and Craig's "Introduction to Mathematical Statistics" (4th edition was much better than the ones after it, imo). But if you're looking to learn prob/stats for applications to ML, most ML textbooks have a chapter or two reviewing the relevant stuff. I liked…
on “Ask HN: What are your favorite statistics and probability textbooks?” ↗…remind myself how certain analysis proofs go. Linear Algebra Strang, Intro to LA is great. Start with this one Strang, LA and learning from data. Will be tough without the first book Stats Hogg, Introduction to Mathematical Statistics Gelman et al, BDA3 for Bayes ML Bishop PRML and Elements of statistical learning. Do the exercises. Build the algos in Python.
on “Ask HN: How to learn math from zero for adults?” ↗…I mostly need Probability, Statistics, Calculus and Linear Algebra. For now I'm studying precalc (Stewart). Next steps are: Probability: Introduction to Probability - Blitzstein & Hwang. Statistics: Introduction to Mathematical Statistics - Hogg & al. Calculus: Calculus, Early Transcendentals - James Stewart & al. Linear Algebra: Introduction to Linear Algebra - Gilbert Strang. What are your picks in those subject? Are these enough?…
on “Ask HN: What are the best textbooks to study in order to learn math for ML?” ↗When I was taking a class in Statistical Inference, we used a combination of Statistical Inference (Casella and Berger), Introduction to Mathematical Statistics (Hogg and Craig) and Probability and Statistics (Degroot and Schervish). If you're still interested in learning about Fisher Information and the Cramer-Rao Lower Bound, you can refer to pages 514 - 521…
on “All of Statistics, by Larry Wassserman (2013) [pdf]” ↗I feel like you must be a using a wrong approach to searching for mathematics. In your case I would search for a script or book with title "Introduction to probabilify theory" or "Introduction to mathematical statistics". Then you skim through it to see if you can find an analysis of your problem. If not, you can hopefully find out what the right keywords are to then find a more advanced script or book for the specific…
on “Math writing is dull when it neglects the human dimension” ↗…books are also good. Data Analysis... https://sites.stat.columbia.edu/gelman/arm/ Regression and Other Stories: https://avehtari.github.io/ROS-Examples/ Wasserman's All of Statistics is a really good introduction to mathematical statistics (the Gelman stuff above are more practically and analytically focused). But yeah, it would probably be easier to find a good statistics course at a local university and try to audit it or do it at night.
on “How linear regression works intuitively and how it leads to gradient descent” ↗