The characteristic function of a random variable is . Useful for proving central limit theorems.
The characteristic function of independent random variables is the product of the individual characteristic functions.
- active statistical inference
- adjusters
- adversarial contamination model
- alpha-divergence
- anisotropic distribution
- anti-concentration
- anytime-valid
- anytime-valid p-values
- asymptotic confidence sequences
- Banach space
- bandits
- basic inequalities
- basic matrix inequalities
- Bayes factors
- Bayesian decision theory
- Bayesian interpretation of probability
- Bayesian nonparametrics
- Bayesian parametrics
- Bayesian statistics
- Bernstein von-Mises theorem
- Berry-Esseen bounds
- best-arm identification
- betting strategies
- BH procedure
- bootstrapping
- bounded difference inequalities
- bounded scalar concentration
- calibration
- Catoni-Giulini M-estimator
- causal inference
- cdf concentration
- cdf estimation
- central limit theorems
- chaining
- characteristic function
- Chernoff method
- chi-squared divergence
- CLTs in Banach spaces
- coarsened filtrations can increase power
- comparing forecasters by betting
- concentration in Banach spaces
- concentration inequalities
- concentration of functions
- concentration of measure
- concentration of self-bounding functions
- concentration via convex optimization
- concentration via covering
- conditional independence testing
- confidence intervals
- confidence sequences
- confidence sequences for convex functionals
- confidence sequences for quantiles
- confidence sequences via conjugate mixtures
- confidence sequences via predictable plug-ins
- conformal p-value
- conformal prediction
- conjugate transpose
- contextual bandit
- covering and packing
- Cramer-Rao lower bound
- credible intervals
- current statistical practice combines the Fisherian and Neyman-Pearson perspectives
- deep density estimation
- density estimation
- differential privacy
- Dirichlet process
- distributional distance
- Donsker class
- Doob's maximal inequality
- doubly robust estimator
- duality between hypothesis tests and CIs
- Dudley chaining
- Dudley's entropy bound
- e-BH procedure
- e-process
- e-value
- e-value calibrators
- e-values enable post-hoc hypothesis testing
- Efron-Stein inequality
- empirical Bernstein bounds
- empirical process theory
- empirical risk minimization
- ensemble learning
- entropy number
- ergodic theorems
- estimating means by betting
- evidence against the null
- evidence is quantifiable in small-worlds
- exchangeable distribution
- exponential families
- exponential inequalities
- external randomization
- f-divergence
- FDR control
- Fisher information
- Fisher information distance
- Fisher's paradigm
- fixed-time
- fork-convex
- foundations of statistics
- frequentist interpretation of probability
- frequentist statistics
- from boundedness to variance adaptivity
- from independence to iid
- game theory
- game-theoretic convergence of opinions
- game-theoretic hypothesis testing
- game-theoretic LLN
- game-theoretic probability
- game-theoretic statistics
- Gaussian complexity
- Gaussian process
- Gaussian process regression
- Gaussian sequence model
- generalized linear model
- generic chaining
- Glivenko-Cantelli class
- goodness-of-fit test
- GRO e-variable
- GROW e-variable
- growth rate conditions in sequential testing
- heavy-tailed concentration
- heavy-tailed maximal inequalities
- Hellinger distance
- Hermitian matrix
- hilbert space
- histograms
- Hölder space
- Huber contamination model
- hypothesis testing
- ideal metrics
- infinitely divisible distribution
- information processing inequality
- information theory
- instrumentalist theory of probability
- integral probability metric
- interpolating between Markov and Chernoff
- inverse problems
- irregular problems in hypothesis testing
- isotropic distributions
- issues with p-values
- Jeffreys prior
- Jeffreys' paradigm of hypothesis testing
- Karlin-Rubin theorem
- Kelly betting
- kernel density estimation
- kernel MMD
- kernel regression
- kernel trick
- KL divergence
- knn
- KS distance
- lady tasting tea
- law of likelihood
- laws of large numbers
- laws of the iterated logarithm
- learning theory
- light-tailed maximal inequalities
- light-tailed, unbounded scalar concentration
- likelihood principle
- likelihood-ratio test
- Lindeberg-Feller CLT
- Lindeberg-Levy CLT
- Linear Regression
- linear smoothers
- local differential privacy
- local polynomial regression
- Loewner order
- log-concave distribution
- Lp norm
- Lyapunov CLT
- M-estimation
- marginal consistency
- Markov chain concentration
- Markovian alternatives
- martingale CLT
- martingale concentration
- martingale dependence
- matrix inequalities
- matrix martingale inequalities
- maximal inequalities
- maximizing log-wealth
- Mayo's error statistics
- MCMC
- mean estimation
- median-of-means
- Mercer kernel
- merging e-values
- method of moments for concentration
- method of moments for estimation
- metric entropy
- metric space
- MGF
- minimal sufficiency
- MLE
- model selection
- model-X assumption
- Monge formulation
- monotone likelihood ratio
- multi-armed bandits
- multi-group calibration
- multi-group consistency
- multiple testing
- multivariate concentration
- multivariate heavy-tailed mean estimation
- multivariate light-tailed concentration
- mutual information
- Nash equilibrium
- negative correlation can improve concentration
- Neyman-Pearson lemma
- Neyman-Pearson lemma for discrete distributions
- Neyman-Pearson paradigm
- Neyman-Pearson paradigm with losses
- nonparametric classification
- nonparametric density estimation
- nonparametric regression
- numeraire e-variable
- online calibration
- online gradient descent
- online marginal estimation
- Online Newton Step
- operator norm inequalities
- optimal transport
- optimal transport costs
- optimality of Markov and Chebyshev
- optimization perspective on Markov's inequality
- optional continuation
- optional stopping
- Orlicz norm
- p-hacking
- p-value
- PAC learning
- PAC-Bayes
- parametric density estimation
- parametric versus nonparametric statistics
- partitions and trees
- permutation test
- permutation testing by betting
- Petrov's CLT template
- pinball loss
- Pinelis approach to concentration
- portfolio optimization
- post-hoc confidence sequences via e-processes
- post-hoc hypothesis testing
- post-hoc hypothesis testing with losses
- post-hoc valid confidence sequences
- PRDS
- prediction-powered inference
- proper scoring rule
- quantile estimation
- quantitative CLT template with ideal metrics
- Rademacher complexity
- randomized inequalities
- Rao-Blackwell theorem
- regret minimization
- REGROW e-variable
- representer theorem
- reverse information projection (RIPr)
- RKHS
- rkhs regression
- robust statistics
- Royall's three questions
- safe, anytime-valid inference (SAVI)
- scalar heavy-tailed mean estimation
- score function
- self-normalized concentration
- self-supervised learning
- semi-supervised learning
- sequential hypothesis testing
- sequential probability ratio test
- sequential statistics
- small worlds vs large worlds
- splines
- squared error
- statistical contract theory
- statistical decision theory
- statistical inference
- stitching for LIL rates
- stopping-time
- strong approximations
- sub-exponential distributions
- sub-Gaussian distributions
- sub-Gaussian process
- sub-psi process
- submartingale
- sufficiency and the likelihood
- sufficient statistic
- supermartingale
- supervised learning
- survey sampling
- t-test
- techniques for multivariate concentration
- test-martingale
- testing by betting—composite vs composite
- testing by betting—simple vs composite
- testing by betting—simple vs simple
- testing by betting—two-sample testing
- testing exchangeability
- testing forecasters by betting
- testing group invariance
- the missing factor in Hoeffding's bounds
- the problem of approximate inference in deep learning
- time-uniform
- total variation distance
- trimmed mean estimator
- truncation-based estimators
- two-sample testing
- u-statistics
- UCB algorithms
- uncertainty quantification
- uniform convergence bounds
- uniformly most powerful test
- universal inference
- unsupervised learning
- v-statistics
- Vapnik-Chervonenkis theory
- variational approach to concentration
- variational inference
- Ville's inequality
- Wald interval
- Wald test
- Warner's randomized response
- Wasserstein Distance
- wavelets
- weighted least squares
- zero sum game