References🔗

Bibliography (7)

• Herbert Federer, 1969. “Geometric Measure Theory”. In Springer. (Grundlehren der mathematischen Wissenschaften, vol. 153)
  Cited from (2)

  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
• Keith Ball (1993). “The reverse isoperimetric problem for Gaussian measure”. Discrete and Computational Geometry. 10(4), pp. 411–420.
  Cited from (13)

  • Document root
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
• Louis H. Y. Chen and Qi-Man Shao (2001). “A non-uniform Berry--Esseen bound via Stein's method”. Probability Theory and Related Fields. 120(2), pp. 236–254.
  Cited from (3)

  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.8: Reflection and the nonuniform theorem
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.2: Uniform approximation and leave-one-out concentration
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.2: Uniform approximation and leave-one-out concentration
• Louis H. Y. Chen and Qi-Man Shao, 2005. “Stein's method for normal approximation”. In An Introduction to Stein's Method, pp. 1--59. (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 4)
  Cited from (17)

  • Document root
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.6: Estimates for the residual terms
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.6: Estimates for the residual terms
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.6: Estimates for the residual terms
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.6: Estimates for the residual terms
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.6: Estimates for the residual terms
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.3: Exponential concentration
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.3: Exponential concentration
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.4: One-sided truncation
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.8: Reflection and the nonuniform theorem
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.8: Reflection and the nonuniform theorem
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.5: Stein exchange and residual decomposition
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.5: Stein exchange and residual decomposition
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.7: The central nonuniform estimate
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.1: The half-line Stein equation
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.1: The half-line Stein equation
  • Chapter 1: Nonuniform Berry--Esseen bounds, Section 1.2: Uniform approximation and leave-one-out concentration
• Martin Raič (2019). “A multivariate Berry--Esseen theorem with explicit constants”. Bernoulli. 25(4A), pp. 2824–2853.
  Cited from (8)

  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
  • Chapter 2: Normal approximation over convex sets, Section 2.4: Signed distance and coarea
• Vidmantas Bentkus (2003). “On the dependence of the Berry--Esseen bound on dimension”. Journal of Statistical Planning and Inference. 113(2), pp. 385–402.
  Cited from (3)

  • Chapter 2: Normal approximation over convex sets, Section 2.1: Convex distance and smooth cutoffs
  • Chapter 2: Normal approximation over convex sets, Section 2.1: Convex distance and smooth cutoffs
  • Chapter 2: Normal approximation over convex sets, Section 2.1: Convex distance and smooth cutoffs
• Vidmantas Bentkus (2004). “A Lyapunov-type bound in R^d”. Teoriya Veroyatnostei i ee Primeneniya. 49(2), pp. 400–410.
  Cited from (30)

  • Document root
  • Chapter 2: Normal approximation over convex sets, Section 2.5: Ball's Gaussian perimeter theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.10: Bentkus's convex-set theorem
  • Chapter 2: Normal approximation over convex sets, Section 2.1: Convex distance and smooth cutoffs
  • Chapter 2: Normal approximation over convex sets, Section 2.1: Convex distance and smooth cutoffs
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.2: Gaussian companions and rotation
  • Chapter 2: Normal approximation over convex sets, Section 2.7: Gaussian density calculus
  • Chapter 2: Normal approximation over convex sets, Section 2.7: Gaussian density calculus
  • Chapter 2: Normal approximation over convex sets, Section 2.7: Gaussian density calculus
  • Chapter 2: Normal approximation over convex sets, Section 2.7: Gaussian density calculus
  • Chapter 2: Normal approximation over convex sets, Section 2.6: Smoothing convex indicators
  • Chapter 2: Normal approximation over convex sets, Section 2.8: Taylor remainders and angle splitting
  • Chapter 2: Normal approximation over convex sets, Section 2.8: Taylor remainders and angle splitting
  • Chapter 2: Normal approximation over convex sets, Section 2.8: Taylor remainders and angle splitting
  • Chapter 2: Normal approximation over convex sets, Section 2.8: Taylor remainders and angle splitting
  • Chapter 2: Normal approximation over convex sets, Section 2.8: Taylor remainders and angle splitting
  • Chapter 2: Normal approximation over convex sets, Section 2.9: The identity-covariance replacement induction
  • Chapter 2: Normal approximation over convex sets, Section 2.9: The identity-covariance replacement induction
  • Chapter 2: Normal approximation over convex sets, Section 2.9: The identity-covariance replacement induction
  • Chapter 2: Normal approximation over convex sets, Section 2.3: Whitening and covariance normalization
  • Chapter 2: Normal approximation over convex sets, Section 2.3: Whitening and covariance normalization
  • Chapter 2: Normal approximation over convex sets, Section 2.3: Whitening and covariance normalization
  • Chapter 2: Normal approximation over convex sets, Section 2.3: Whitening and covariance normalization