A proof of the Gamma test

By Dafydd Evans, Antonia J. Jones. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002

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Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database (2011, methodology): “This condition is satisfied whenM ! 1 as proven in Evans and Jones (2002). The slope A gives a crude estimate of the complexity of the unknown surface of the regression function, f(x).”
Laws of large numbers in stochastic geometry with statistical applications (2007, methodology): “,Wn is the so-called Gamma statistic [5] based on nearest neighbours; one can consider a similar statistic based on kth nearest neighbours.”
Asymptotic moments of near–neighbour distance distributions (2002, background): “In another paper (Evans & Jones 2002) we show that bounded functions of a point and its kth nearest neighbour satisfy a weak law of large numbers with explicit bounds.”
Uncertainty analysis of developed ANN and ANFIS models in prediction of carbon monoxide daily concentration (2010, methodology): “A formal mathematical justification of this method can be found in Evans and Jones (2002).”
Gaussian Limts for Random Geometric Measures (2007, background): “There are interesting potential applications of the theory with non translation-invariant ξ to topics in multivariate statistics such as nonparametric density estimation and nonparametric regression (4; 2; 6), but these are not easy to describe briefly.”