Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US

Nagahara, Yuichi

doi:10.1007/s10690-011-9138-4

Cited by 1 publication

(2 citation statements)

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“…(19). The probability density functions of PD-system are solutions of the following differential equation (Pearson 1920;Elderton 1953;Hald 2007;Nagahara 2007Nagahara , 2011Friori and Zenga 2009;Dzhun' 2011;Xi et al 2012)…”

Section: Pearson Distributionsmentioning

confidence: 99%

“…The problem is a general one and from such point of view it is considered, for example, in Mooijaart (1985); Klein and Moosbrugger (2000); Mukhopadhyay (2005). It is also an issue discussed in the applied statistics, for example, in marketing Andreassen et al (2006) and in econometrics Nagahara (2011). The influence of deviation of an empirical distribution from the normal distribution on LS-estimates in the case of geodetic networks was discussed in Gleinsvik (1971Gleinsvik ( ,1972 and Wiśniewski (1985).…”

Section: Introductionmentioning

confidence: 99%

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M-estimation with probabilistic models of geodetic observations

Wiśniewski

2014

J Geod

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The paper concerns M-estimation with probabilistic models of geodetic observations that is called M P estimation. The special attention is paid to M P estimation that includes the asymmetry and the excess kurtosis, which are basic anomalies of empiric distributions of errors of geodetic or astrometric observations (in comparison to the Gaussian errors). It is assumed that the influence function of M P estimation is equal to the differential equation that defines the system of the Pearson distributions. The central moments μ k , k = 2, 3, 4, are the parameters of that system and thus, they are also the parameters of the chosen influence function. The M P estimation that includes the Pearson type IV and VII distributions (M PD(l) method) is analyzed in great detail from a theoretical point of view as well as by applying numerical tests. The chosen distributions are leptokurtic with asymmetry which refers to the general characteristic of empirical distributions. Considering M-estimation with probabilistic models, the Gram-Charlier series are also applied to approximate the models in question (M G−C method). The paper shows that M P estimation with the application of probabilistic models belongs to the class of robust estimations; M PD(l) method is especially effective in that case. It is suggested that even in the absence of significant anomalies the method in question should be regarded as robust against gross errors while its robustness is controlled by the pseudo-kurtosis.

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