| Introduction | 第1-40页 |
| ·Rudiments of the theory of large deviations | 第8-14页 |
| ·Origins and definitions | 第8-10页 |
| ·Cramer functional and Gartner-Ellis theorem | 第10-12页 |
| ·From w*-LDP to LDP : exp-tight* and the contraction principle | 第12-13页 |
| ·Several references about applications of the theory of large deviations | 第13-14页 |
| ·kernel density estimation | 第14-19页 |
| ·Motivation | 第14-15页 |
| ·Definition and references | 第15-19页 |
| ·Approach of partition of Devroye | 第19页 |
| ·Presentation of main results | 第19-32页 |
| ·In the i.i.d. case (Chapter 1) | 第19-21页 |
| ·In the φ-mixing process case (Chapter 2) | 第21-24页 |
| ·In the uniformly ergodic Markov process case (Chapter 3) | 第24-28页 |
| ·In the reversible Markov process case (Chapter 4) | 第28-32页 |
| Bibliography | 第32-40页 |
| 1 Large deviations and deviation inequality for kernel density estimator in L~1 (R~d)-distance (Published in: Development of Modern Statistics and Related Topics) | 第40-50页 |
| ·Introduction | 第40-41页 |
| ·Main results | 第41-43页 |
| ·Proofs of the main results | 第43-47页 |
| ·Proof of Proposition 1.1 | 第43-44页 |
| ·Proof of Theorem 1.2 | 第44-46页 |
| ·Proof of Theorem 1.3 | 第46-47页 |
| Bibliography | 第47-50页 |
| 2 The exponential convergence of kernel density estimator in L~1 for φ-mixing processes (Published in: Annales de L'I.S.U.P.) | 第50-60页 |
| ·Introduction | 第50-52页 |
| ·Main results | 第52页 |
| ·Some deviation inequalities for φ-mixing sequences | 第52-54页 |
| ·Proofs of the main results | 第54-58页 |
| ·Proof of Theorem 4.2 | 第54页 |
| ·Proof of Theorem 2.2 | 第54-58页 |
| ·Concluding remarks | 第58页 |
| Bibliography | 第58-60页 |
| 3 Large deviations of kernel density estimator in L~1(R~d) for uniformly ergodic Markov processes (Published in: Stochastic Processes and their Applications) | 第60-88页 |
| ·Introduction | 第60-62页 |
| ·Main results | 第62-66页 |
| ·Several lemmas | 第66-75页 |
| ·Proof of Theorem 3.1 | 第75页 |
| ·Proof of Theorem 3.2 | 第75-78页 |
| ·Proof of Theorem 3.3 | 第78-84页 |
| ·Proof of part (a) in Theorem 3.3 | 第78-82页 |
| ·Proof of Part (b) in Theorem 3.3 | 第82-83页 |
| ·Proof of Part (c) in Theorem 3.3 | 第83-84页 |
| ·Proof of Theorem 3.4 | 第84-85页 |
| Bibliography | 第85-88页 |
| 4 Large deviations of kernel density estimator in L~1(R~d) for reversible Markov processes (To be published in: Bernoulli) | 第88-107页 |
| ·Introduction | 第88-90页 |
| ·Main results | 第90-93页 |
| ·Preliminary lemmas | 第93-97页 |
| ·Proof of Theorem 4.1 | 第97-100页 |
| ·Upper bound | 第97-98页 |
| ·Lower bound | 第98-100页 |
| ·Proof of Theorem 4.2 | 第100-103页 |
| ·Proof of Theorem 4.3 | 第103-104页 |
| ·Proof of Theorem 4.4 | 第104-105页 |
| Bibliography | 第105-107页 |
