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 Cram&eacute;r-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-J&oslash;rgensen-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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