Statistical Inference via Convex Optimization (eBook)

Anatoli Juditsky, Arkadi Nemirovski (Autoren)

eBook Download: PDF

2020
656 Seiten
Princeton University Press (Verlag)
978-0-691-20031-6 (ISBN)

Infos

This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences.Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems-sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals-demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems.Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.

Produkt-Details

• Erscheint lt. Verlag: 7.4.2020
• Reihe/Serie: Princeton Series in Applied Mathematics
• Reihe/Serie: Princeton Series in Applied Mathematics
• Zusatzinfo: 40 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Schlagworte: Accuracy and precision • Affine space • All of Nonparametric Statistics • Approximation • Asymptotic Methods in Statistical Decision Theory • Bayesian • Bias of an estimator • Binary search algorithm • bisection algorithm • Bounded set (topological vector space) • Candidate solution • Change detection • Characteristic function (probability theory) • compressed sensing • Computation • computational complexity theory • concave function • conditional expectation • Conditional probability distribution • conic programming • Convergence of random variables • Convex cone • convex function • convex hull • Convex Optimization • convex set • Convex sets • Covariance matrix • Dantzig selector • Differentiable function • Dimension (vector space) • Discrete Cosine Transform • Duality • Duality (optimization) • ell-1-norm minimization • Empirical probability • Error analysis (Mathematics) • Error Function • Estimating Functions • estimation • Estimation theory • Estimator • Function (mathematics) • gaussian noise • Gaussian observations • Has'minskii • Hellinger distance • Ibragimov • Independence (probability theory) • Inequality (mathematics) • inference • Infimum and supremum • Introduction to Nonparametric Estimation • Invertible matrix • Joint probability distribution • Lagrange duality • lasso selector • Least Squares • Le Cam • Likelihood Function • Linear dynamical system • Linear Function • Linear Inequality • Linear map • Linear Matrix Inequality • Linear Programming • linear regression • Lipschitz continuity • Logistic Regression • Mathematical Induction • Mathematical Optimization • mathematical practice • Maxima and minima • Measure (mathematics) • Measurement • Minimization • Moment-generating function • Moment (mathematics) • Monte Carlo Method • Multivariate normal distribution • N-convex function • Non-linear least squares • Nonparametric regression • Nonparametric Statistics • Norm (mathematics) • NP-hardness • Observational error • optimization problem • Parameter • Parametric family • Poisson distribution • Preference (economics) • Probability • Probability Distribution • Probability of error • Probability space • Probability Theory • Proportionality (mathematics) • P versus NP problem • random matrix • Random Variable • Rate of Convergence • rectangle • Restricted isometry property • saddle points • Sampling (Statistics) • signal plus noise • signal-to-noise • singular value decomposition • Sparse matrix • Statistical estimation • Statistical hypothesis testing • Statistical Inference • statistical significance • Statistics • stochastic approximation • Stochastic matrix • stochastic optimization • Subset • Tsybakov • Uniform distribution (discrete) • unobserved signal • Upper and lower bounds • Variable (mathematics) • Variable selection • Variational inequality • Wasserman
• ISBN-10: 0-691-20031-9 / 0691200319
• ISBN-13: 978-0-691-20031-6 / 9780691200316