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Statistics Graduate Level · Lessons

Statistics Graduate Level lessons

11 sections · 80 skills · work through the full outline skill by skill — read the long-form lesson or flip through the slide-style version.
Long-form lessonsSlide-style lessons

Statistics Graduate Level

Practice 80 skills across this outline.

Recommended next
Standard Distribution Results
Proof, Derivation & Problem-Solving Tools
Long-form lesson
Weighting distribution
20 categories
Proof, Derivation & Problem-Solving Tools
9%
Asymptotic Theory
9%
Interval Estimation
9%
Simulation, Resampling & Computation
9%
Statistical Inference · Point Estimation Theory
5%
Bayesian Statistics · Bayesian Foundations
5%

Skills

The comprehensive taxonomy of statistics graduate level — drill into a card to work its skills.

Proof, Derivation & Problem-Solving Tools

5 core skills9% total weight
0/5 completed
5 skills to mastery
1
Standard Distribution ResultsRecommended
Long-form
2
Common PitfallsAvailable
Long-form
3
Taylor Expansions for ApproximationsAvailable
Long-form
4
Likelihood ManipulationAvailable
Long-form
5
Computing via ConditioningAvailable
Long-form

Probability Foundations · Common Distributions and Transforms

5 core skills3% total weight
0/5 completed
5 skills to mastery
1
Conditional Distributions & MarginalizationAvailable
Long-form
2
MGF & Characteristic FunctionsAvailable
Long-form
3
Transformations & JacobiansAvailable
Long-form
4
Order StatisticsAvailable
Long-form
5
Multivariate DistributionsAvailable
Long-form

Probability Foundations · Measure-Free Probability Toolkit

5 core skills3% total weight
0/5 completed
5 skills to mastery
1
Sigma-Algebras & Probability AxiomsAvailable
Long-form
2
Expectation PropertiesAvailable
Long-form
3
Random Variables & DistributionsAvailable
Long-form
4
Independence & ConditioningAvailable
Long-form
5
Conditional Probability & ExpectationAvailable
Long-form

Probability Foundations · Inequalities and Bounds

3 core skills2% total weight
0/3 completed
3 skills to mastery
1
Jensen's InequalityAvailable
Long-form
2
Markov & Chebyshev InequalitiesAvailable
Long-form
3
Union Bounds & ConcentrationAvailable
Long-form

Statistical Inference · Point Estimation Theory

5 core skills5% total weight
0/5 completed
5 skills to mastery
1
Unbiased Estimation & UMVUEAvailable
Long-form
2
Consistency & EfficiencyAvailable
Long-form
3
Fisher Information & Cramér-Rao BoundAvailable
Long-form
4
Method of Moments & MLEAvailable
Long-form
5
Bias, Variance & MSEAvailable
Long-form

Statistical Inference · Likelihood and Estimation Framework

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Identifiability & ParameterizationAvailable
Long-form
2
Sufficient StatisticsAvailable
Long-form
3
Likelihood & Score FunctionAvailable
Long-form
4
Exponential FamiliesAvailable
Long-form

Advanced Topics in Graduate Statistics · Time Series and Stochastic Processes

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Stationarity & AutocorrelationAvailable
Long-form
2
AR & ARMA ModelsAvailable
Long-form
3
Forecasting & Prediction IntervalsAvailable
Long-form

Advanced Topics in Graduate Statistics · Nonparametric and Regularization

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Kernel Density EstimationAvailable
Long-form
2
Rank-Based TestsAvailable
Long-form
3
Ridge & Lasso RegularizationAvailable
Long-form

Advanced Topics in Graduate Statistics · Multivariate Methods

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Covariance Matrices & Eigen DecompositionAvailable
Long-form
2
Hotelling's T²Available
Long-form
3
Principal Component Analysis (PCA)Available
Long-form
4
Multivariate Normal DistributionAvailable
Long-form

Bayesian Statistics · Bayesian Foundations

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Conjugate PriorsAvailable
Long-form
2
Posterior Predictive DistributionAvailable
Long-form
3
Bayesian Inference BasicsAvailable
Long-form
4
Posterior Summaries & Credible IntervalsAvailable
Long-form

Bayesian Statistics · Computation

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Gibbs & Metropolis-Hastings SamplingAvailable
Long-form
2
MCMC Convergence DiagnosticsAvailable
Long-form
3
MCMC ConceptsAvailable
Long-form

Asymptotic Theory

4 core skills9% total weight
0/4 completed
4 skills to mastery
1
M-EstimatorsAvailable
Long-form
2
Influence FunctionsAvailable
Long-form
3
Asymptotic Normality of MLEAvailable
Long-form
4
Sandwich Variance & Robust SEAvailable
Long-form

Convergence & Limit Theorems · Core Theorems

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Slutsky's & Continuous Mapping TheoremsAvailable
Long-form
2
Law of Large NumbersAvailable
Long-form
3
Delta MethodAvailable
Long-form
4
Central Limit TheoremAvailable
Long-form

Convergence & Limit Theorems · Modes of Convergence

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Convergence in LpAvailable
Long-form
2
Convergence Mode RelationshipsAvailable
Long-form
3
Convergence in Probability & Almost SureAvailable
Long-form
4
Convergence in DistributionAvailable
Long-form

Hypothesis Testing · Multiple Testing and Decision Concepts

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
False Discovery Rate (FDR)Available
Long-form
2
Loss Functions & Decision TheoryAvailable
Long-form
3
Family-Wise Error Rate & BonferroniAvailable
Long-form

Hypothesis Testing · Neyman–Pearson and Likelihood Ratio Tests

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
p-Values & Test InversionAvailable
Long-form
2
Type I/II Errors & PowerAvailable
Long-form
3
Neyman-Pearson LemmaAvailable
Long-form
4
Likelihood Ratio Tests & Wilks' TheoremAvailable
Long-form

Interval Estimation

4 core skills9% total weight
0/4 completed
4 skills to mastery
1
Bootstrap Confidence IntervalsAvailable
Long-form
2
Likelihood-Based CIsAvailable
Long-form
3
Pivotal Quantities & Exact CIsAvailable
Long-form
4
CIs from Asymptotic NormalityAvailable
Long-form

Linear Models and GLMs · Generalized Linear Models

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Deviance & Goodness-of-FitAvailable
Long-form
3
Logistic RegressionAvailable
Long-form
4
Poisson RegressionAvailable
Long-form

Linear Models and GLMs · Matrix Linear Regression

5 core skills5% total weight
0/5 completed
5 skills to mastery
1
Inference for Regression CoefficientsAvailable
Long-form
2
Linear Regression in Matrix FormAvailable
Long-form
3
Least Squares & Normal EquationsAvailable
Long-form
4
Gauss-Markov Theorem & BLUEAvailable
Long-form
5
Regression DiagnosticsAvailable
Long-form

Simulation, Resampling & Computation

4 core skills9% total weight
0/4 completed
4 skills to mastery
1
Permutation TestsAvailable
Long-form
2
Simulation for ValidationAvailable
Long-form
3
Monte Carlo EstimationAvailable
Long-form
4
Bootstrap ResamplingAvailable
Long-form