Lecture Notes for Advanced Inference I
===
Table of Contents
---
- [Course Overview](https://hackmd.io/lpRS-QdfQ7Wkgzi3AdTJAg#)
- [0. Pre-requisites from Measure Theory](https://hackmd.io/59od-dO4RJeZC5Go731MBQ?view#)
- [1. Convergence in Probability and Almost Surely - I](https://hackmd.io/Z9u0AgCDSTOwOxmlUPBhoA#)
- [2. Convergence in Probability and Almost Surely - II](https://hackmd.io/7_I5F_3vTHOJHnlhEUVGIQ#)
- [3. Convergence in Distribution - I](/neD5-htKSBqDdnBcLbgm4g)
- [4. Conv. in Dist. - II: Portmanteau's Lemma](/crl1pBQcQFuRYaLS7QHR8A)
- [5. Continuous Mapping \& Prohorov's Theorem](/-Tax_OXOTq6zvV1Y_aDAHA)
- [5A. Quantile Functions](/YV44zt2ZTDSaSai-pOWx_w)
- [6. Helly's, and Markov's Theorem](/b84XJyvIS5umyezOP8urNg)
- [7. Slutsky's Theorem](/3CNzmB8pQNm2--TkFrCoMQ)
- [8. Polya's Theorem, $o_P$ & $O_P$, and Characteristic Functions](/IABskRDPT4e7Yu_0mQ_pYA)
- [9. Levy's Continuity Theorem and Cramér-Wold Device](/O0xEeJW_T7WL_hnEyoflTw)
- [10. On Weak LLN](/h66TYra8TIufZQowBLraGw)
- [11. Metrics on Probability Spaces - I](/gXFvL58WQfCcC3XBMJSvJg)
- [12. CLT in Total Variation Norm](/x0M0FwlJRWGP-zz7EJX_1A)
- [13. Metrics on Probability Spaces - II](/O-85BeqRTxa2LZJT_ApMGQ)
- [14. The Delta Method](/fG4WnKZNRpaoP4T5530roA)
- [15. Some Interesting Applications of the Delta-Method](/yvChyx9mSVKTJlv87hac2g)
- [16. Uniform Delta Method and the Mean Value Theorem for Vector Valued Maps](/vuYDevMkRFSotj0f4FmlvQ)
- [17. Moment Estimators and the Inverse Function Theorem](/eu1-9kJWQIGjZqrShWfh5A)
- [18. Exponential Families and Asymptotic Normality of MLE](/P3nzInebTayPTj-TgQwKug)
- [19. Intro. to M and Z Estimators](/ydR-Fza9QiaHt2XEOSSJ_A)
- [20. Consistency of M and Z Estimators - I](/io2pe1zmSP-C6PZDOhHwTg)
- [21. Glivenko-Cantelli Theorems](/ChPlABcMR4O_mb7iynWXyQ)
- [22. 2-means on the Real Line - Consistency](/L3SD7SFhSNWL5--jAu_OoA)
- [23. Consistency of M and Z Estimators - II](/jPEp9EQ-SuSqeouixmhE2g)
- [24. Current Status Data - MLE Consistency](/LTDLGuTSS92c6PR8TVAaQw)
- [25. ~~Hoffmann-Jørgensen-Dudley Theory of Weak Convergence~~](/17Ik5KJDSDm3M0t-2CMg0g)
- [26. Some Results from Empirical Process Theory](/ccBr7FgtTkalVC5SeXHOnQ)
- [27. Asymptotic Normality of Z-Estimators](/CKyq-j2hRHub8jzlJnIq6w)
- [28. Asymptotic Normality in the Exponential Frailty Model](/V4pv9eqVQRqFu0jyYaaJnw)
- [29. Bahadur Representation and Asymptotic Normality of Quantiles](/szdEDGLWQYqWrGTt_OXsEw)
- [30. Asymptotic Normality of M-Estimators](/hX_oEu-LSfyfNGzVplGkiw)
- [31. Differentiability in Q. M.](/aWFFvdJmRYWm1tZSIgubow)
- [32. Uniformly Consistent Tests and Estimators](/LcJsrKhcQLGKvowtu-T5rA)
- [33. Contiguity](/ynau-d3pTt6zJd4sxfjJGQ) <!--[(/Sv1nYJ8hSJy-7g0cIrPvNQ) Old version -->
- [34. Asymptotic Normality of MLEs](/Xj2ZqkdQRx2Ro_B56eqc7A)
[35. Bernstein-von Mises Theorem](/TgA8eUTEQ6qlId6fbg0WUQ) <!--(/0Ne88t0xRVqeyfzestLqEQ) -->
- [36. :no_pedestrians: Doob’s consistency theorem](/hf9ystajQw6uT3gvJjBkuQ)
- [37. :no_pedestrians: Argmax Theorem](/gSQrZqIYRlaaPuUvkqmfsQ)
- [38. :no_pedestrians: One-Step estimators](/6iD102HyQDCv9JmYbWNQCg)
- [39. :no_pedestrians: Rates of Convergence](/ZvUDjh1hTMeGHhE5D8YJbQ)
<!-- - [40 ](/y6lw17z7Tw-rmi4MGHEJAg) -->
-[Appendix A: Assigned Problems from the Text](/oBfT77z3R8KVsxfVT6_FcQ)
<!-- - [Appendix A: Suggested Problems from the Text](/FNElWENjT4aBCjQ2RG8x5w) -->
- [Appendix B: Problems from the Course](/ASyAmDzkS1C0v9aRR9hfCQ)
- [Appendix C: Quiz solutions](/YuPmOtWmSk2yl6gN5hJvYw)
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