1 Introduction
1.1 Previous Work
2 Preliminaries
2.1 The beta distribution and its relatives
2.2 Hölder-Continuity
2.3 The Distributional Master Theorem
2.4 Adaptive Quickselect
2.5 Cost Measures and Notation
3 Distributional Recurrence
4 Random ranks
4.1 Generic Multiway Partitioning
4.2 Discussion
4.3 Adaptive Methods
5 Asymptotic Approximation for Linear Ranks
6 YBB-Select with Linear Ranks
7 Sesquickselect
7.1 Sesquickselect with larger samples
8 Conclusion
8.1 Future Work
Appendix
A Index of Notation
A.1 Generic Mathematical Notation
A.2 Stochastics-related Notation
A.3 Notation for our Analysis
B Proof of Hölder integration lemma
C Proof of Local Limit Law
D Constants for Sesquickselect
E Optimal Threshold for Sesquickselect
F Proof of Convergence for Linear Ranks
F.1 Derivation of the integral equation
F.2 Proof of convergence
References