Statistics
Mathematical Statistics II
Train on Mathematical Statistics II with 687 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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Course topics
Course topics
Neyman-Pearson testing and power
Consistency, asymptotic normality, and delta methods
Bayesian inference and decision rules
Linear models and projection geometry
Rank and distribution-free methods
Bootstrap, permutation, and simulation-based inference
Practice problems
Try a few Mathematical Statistics II problems, each with a hint.
- A multiple-testing procedure makes R rejections, of which V are rejections of true null… Free with an accountNeyman-Pearson testing and power
- A list can have a controlled expected fraction of false discoveries while a shorter… Free with an accountNeyman-Pearson testing and power
- Let X₁,X₂,… be iid with mean μ and variance 0<σ²<∞ Consistency, asymptotic normality, and delta methods
- Let X₁,…,Xₙ be iid N(θ²,1), with parameter θ ≥ 0 Consistency, asymptotic normality, and delta methods
- A categorical probability vector (P₁,P₂,P₃) has a Dirichlet prior with parameters (1,2,3) Bayesian inference and decision rules
- Choosing a model and then reporting its conditional credible interval can discard a… Bayesian inference and decision rules
- Let X be a fixed n×p matrix with linearly independent columns, and let y ∈ ℝⁿ Linear models and projection geometry
- Let X₁,…,Xₙ be iid from an arbitrary continuous distribution Rank and distribution-free methods
- All random variables below are square-integrable and centered: 𝔼[x]=𝔼[z]=𝔼[y]=0 Linear models and projection geometry
- The sample is x=(1,2,4) with n=3 Bootstrap, permutation, and simulation-based inference