دانلود کتاب Asymptotic Statistics: With a View to Stochastic Processes

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Preface\n1 Score and Information\n 1.1 Score, Information, Information Bounds\n 1.2 Estimator Sequences, Asymptotics of Information Bounds\n 1.3 Heuristics on Maximum Likelihood Estimator Sequences\n 1.4 Consistency of ML Estimators via Hellinger Distances\n2 Minimum Distance Estimators\n 2.1 Stochastic Processes with Paths in Lp(T, t, μ)\n 2.2 Minimum Distance Estimator Sequences\n 2.3 Some Comments on Gaussian Processes\n 2.4 Asymptotic Normality for Minimum Distance Estimator Sequences\n3 Contiguity\n 3.1 Le Cam’s First and Third Lemma\n 3.2 Proofs for Section 3.1 and some Variants\n4 L2-differentiable Statistical Models\n 4.1 Lr -differentiable Statistical Models\n 4.2 Le Cam’s Second Lemma for i.i.d. Observations\n5 Gaussian Shift Models\n 5.1 Gaussian Shift Experiments\n 5.2 Brownian Motion with Unknown Drift as a Gaussian Shift Experiment\n6 Quadratic Experiments and Mixed Normal Experiments\n 6.1 Quadratic and Mixed Normal Experiments\n 6.2 Likelihood Ratio Processes in Diffusion Models\n 6.3 Time Changes for Brownian Motion with Unknown Drift\n7 Local Asymptotics of Type LAN, LAMN, LAQ\n 7.1 Local Asymptotics of Type LAN, LAMN, LAQ\n 7.2 Asymptotic optimality of estimators in the LAN or LAMN setting\n 7.3 Le Cam’s One-step Modification of Estimators\n 7.4 The Case of i.i.d. Observations\n8 Some Stochastic Process Examples for Local Asymptotics of Type LAN, LAMN and LAQ\n 8.1 Ornstein–Uhlenbeck Process with Unknown Parameter Observed over a Long Time Interval\n 8.2 A Null Recurrent DiffusionModel\n 8.3 Some Further Remarks\nAppendix\n 9.1 Convergence of Martingales\n 9.2 Harris RecurrentMarkov Processes\n 9.3 Checking the Harris Condition\n 9.4 One-dimensional Diffusions\nBibliography\nIndex