Exponential Approximation by Stein's Method and Spectral Graph Theory

By Sourav Chatterjee, Jason E. Fulman, Adrian Röllin. 2006

73 citations recorded by the source corpus.

General Berry-Esseen bounds are developed for the exponential distri- bution using Stein's method and a new concentration inequality approach. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Johnson graph has an exponential limit.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cf9dcb7e5ba282120599eb597a99532fbbfe6edc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Robert E. Gaunt
2. Nathan Ross
3. Yvik Swan
4. Christophe Ley
5. Gesine Reinert
6. A. Pickett
7. Sourav Chatterjee
8. Jim G. Dai

In Mathematical Physics

1. Nathan Ross
2. Robert E. Gaunt
3. Gesine Reinert
4. Yvik Swan
5. Christophe Ley
6. A. Pickett
7. Sourav Chatterjee
8. Giovanni Peccati

In Statistics and Probability

1. Gesine Reinert
2. Christophe Ley
3. Yvik Swan
4. Robert E. Gaunt
5. Nathan Ross
6. Sourav Chatterjee
7. A. Pickett
8. Lihu Xu

Citations in the corpus

• Variance-Gamma approximation via Stein's method (2013, methodology): “j=1 E [ 1 √ n Y 2 j S (2)f ((3))(STj) + 1 2n Y 2 j ( Tj + 1 √ n Yj ) S(3)f ((4))(ST [9] j ) ]∣∣∣∣ ≤ ‖f ((3))‖ n + ‖f ((4))‖ 2n ( 3 + EX(4) m )3/4( 1 + E|Y (3)| √ n ) .”
• A short survey of Stein's method (2014, methodology): “Further advances were made in the recent manuscript of Röllin [75].”
• Stein’s density approach and information inequalities (2012, background): “We refer to [15] for more examples and for an interesting overview of the relationships between these probability metrics.”
• Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model (2009, unknown): “NON-NORMAL APPROXIMATION 21 E|1 − (c0/2)E((W −W )(2)|W )| = O(n), E|W |(3) = O(1) Applying Theorem 1.”
• Fundamentals of Stein's method (2011, methodology): “An alternative approach (followed in [21, 22]) is to use exchangeable pairs with a modified a-Stein condition.”
• Chi-square approximation by Stein's method with application to Pearson's statistic (2015, methodology): “Over the years, Stein’s method has been extended to many other distributions, such as the Poisson [5], multinomial [20], exponential [4], [27], Laplace [29], variance-gamma [14], and the gamma distribution [21], [25], which we develop further in this paper.”