Details

Autor(en) / Beteiligte

• Székely, Gábor J.
• Rizzo, Maria L.

Titel

Goodness-of-Fit

Ist Teil von

• The Energy of Data and Distance Correlation, 2023, Vol.1, p.59-82

Auflage

1

Ort / Verlag

CRC Press

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• A one-sample goodness-of-fit statistic is designed to measure the distance between a hypothesized distribution F 0 and the distribution F from which an observed d-dimensional random sample x 1 , ... , x n is drawn, d ≥ 1 . Suppose that the characteristic function of F 0 is f ^ 0 , the empirical characteristic function of the sample is f ^ n , X , X ′ ∈ ℝ d are iid with cdf F 0 and E | X | d < ∞ . The energy test statistic for the goodness-of-fit test H 0 : F = F 0 vs H 1 : F ≠ F 0 is 5.1 n   E n , d : = n c d ∫ ℝ d | f ^ n ( t ) − f ^ 0 ( t ) | 2 | t | d + 1   d t = = n 2 n ∑ j = 1 n E | x j − X | d − E | X − X ′ | d − 1 n 2 ∑ j , k = 1 n | x j − x k | d ,