Estimation, Method of Moments

Bowman, K. O.; Shenton, L. R.

doi:10.1002/0471667196.ess1618

Cited by 23 publications

(14 citation statements)

References 20 publications

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“…In addition, estimates of distribution parameters obtained by the method of moments may be less precise than those obtained by other estimation procedures such as the method of maximum likelihood (MLE). Bowman and Shenton (1985) present a brief account of the development of the method of moments and its applications. The Generalised Method of Moments (GMM) can encompass the MLE approach as a special case and overcomes many of the problems identified with the classical method when analysing large data sets 13 .…”

Section: Methodsmentioning

confidence: 99%

An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000

Gettinby¹,

Sinclair²,

Power³

et al. 2004

Business Fin & Account

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This paper seeks to characterise the distribution of extreme returns for a UK share index over the years 1975 to 2000. In particular, the suitability of the following distributions is investigated: Gumbel, Frechet, Weibull, Generalised Extreme Value, Generalised Pareto, Log-Normal and Generalised Logistic. Daily returns for the FT All Share index were obtained from Datastream, and the maxima and minima of these daily returns over a variety of selection intervals were calculated. Plots of summary statistics for the weekly maxima and minima on statistical distribution maps suggested that the best fitting distribution would be either the Generalised Extreme Value or the Generalised Logistic. The results from fitting each of these two distributions to extremes of a series of UK share returns support the conclusion that the Generalised Logistic distribution best fits the UK data for extremes over the period of the study. The Generalised Logistic distribution has fatter tails than either the log-normal or the Generalised Extreme Value distribution, hence this finding is of importance to investors who are concerned with assessing the risk of a portfolio. Copyright Blackwell Publishers Ltd, 2004.

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Section: Methodsmentioning

confidence: 99%

An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000

Gettinby¹,

Sinclair²,

Power³

et al. 2004

Business Fin & Account

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“…We fitted models 4-7 by maximum likelihood (24). We fitted models 1-3 and 8 by method-of-moments (25), due to a lack of closed form solutions for maximum likelihood estimates of the parameters. The derivation of method of moments estimates for Models 1 and 2 is detailed in S3 Appendix.…”

Section: Methodsmentioning

confidence: 99%

Elementary Integrate-and-Fire Process Underlies Pulse Amplitudes in Electrodermal Activity

Subramanian

Purdon

Barbieri

et al. 2021

Preprint

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Electrodermal activity (EDA) is a direct read-out of sweat-induced changes in the skin’s electrical conductance. Sympathetically-mediated pulsatile changes in skin sweat measured as EDA resemble an integrate-and-fire process, which yields an inverse Gaussian model as the inter-pulse interval distribution. We have previously showed that the inter-pulse intervals in EDA follow an inverse Gaussian distribution. However, the statistical structure of EDA pulse amplitudes has not yet been characterized based on the physiology. Expanding upon the integrate-and-fire nature of sweat glands, we hypothesized that the amplitude of an EDA pulse is proportional to the excess volume of sweat produced compared to what is required to just reach the surface of the skin. We modeled this as the difference of two inverse Gaussian models for each pulse, one which represents the time required to produce just enough sweat to rise to the surface of the skin and one which represents the time requires to produce the actual volume of sweat. We proposed and tested a series of four simplifications of our hypothesis, ranging from a single difference of inverse Gaussians to a single simple inverse Gaussian. We also tested four additional models for comparison, including the lognormal and gamma distributions. All models were tested on EDA data from two subject cohorts, 11 healthy volunteers during 1 hour of quiet wakefulness and a different set of 11 healthy volunteers during approximately 3 hours of controlled propofol sedation. All four models represent simplifications of our hypothesis outperformed other models across all 22 subjects, as measured by Akaike’s Information Criterion (AIC), as well as mean and maximum distance from the diagonal on a quantile-quantile plot. Our broader model set of four simplifications offered a useful framework to enhance further statistical descriptions of EDA pulse amplitudes. Some of the simplifications prioritize fit near the mode of the distribution, while others prioritize fit near the tail. With this new insight, we can summarize the physiologically-relevant amplitude information in EDA with at most four parameters. Our findings establish that physiologically based probability models provide parsimonious and accurate description of temporal and amplitude characteristics in EDA.AUTHOR SUMMARYElectrodermal activity (EDA) is an indirect read-out of the body’s sympathetic nervous system, or fight-or-flight response, measured as sweat-induced changes in the electrical conductance properties of the skin. Interest is growing in using EDA to track physiological conditions such as stress levels, sleep quality, and emotional states. Our previous worked showed that the times in between EDA pulses obeyed a specific statistical distribution, the inverse Gaussian, that arises from the physiology of EDA production. In this work, we build on that insight to analyze the amplitudes of EDA pulses. In an analysis of EDA data recorded in 11 healthy volunteers during quiet wakefulness and 11 different healthy volunteers during controlled propofol sedation, we establish that the amplitudes of EDA pulses also have specific statistical structure, as the differences of inverse Gaussians, that arises from the physiology of sweat production. We capture that structure using a series of progressively simpler models that each prioritize different parts of the pulse amplitude distribution. Our findings show a physiologically-based statistical model provides a parsimonious and accurate description EDA. This enables increased reliability and robustness in analyzing EDA data collected under any circumstance.

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“…(A large K is computationally very costly.) By doing so, Moilanen (1999) was actually combining his maximum simulated likelihood method with another estimation method, termed the method of moments (Bowman and Shenton 1985; for a related application see Snijders and Van Duijn 1997).…”

Section: Methodsmentioning

confidence: 99%

Improved Bayesian Analysis of Metapopulation Data With an Application to a Tree Frog Metapopulation

Braak

Etienne

2003

Ecology

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Metapopulation models are important tools to predict whether a species can persist in a landscape consisting of habitat patches. Here a Bayesian method is presented for estimating parameters of such models from data on patch occupancy in one or more years. Earlier methods were either ad hoc, produced only point estimates, or could only use turnover information. The new method is based on the assumption of quasi‐stationarity, which enables it to use not only turnover data, but also snapshot data. Being Bayesian, the method produces reliable information about the uncertainty of the parameters and model‐based predictions in the form of posterior distributions. It is computationally demanding, but considerably faster than a recently developed Bayesian method extended beyond turnover data. The method is compared with existing methods (placed in a Bayesian framework) by fitting an extended incidence function model to a data set on a tree frog metapopulation with many missing values and by predicting its viability, mean occupancy, and turnover rate after 100 yr. Corresponding Editor: O. N. Bjornstad.

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Estimation, Method of Moments

Cited by 23 publications

References 20 publications

An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000

An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000

Elementary Integrate-and-Fire Process Underlies Pulse Amplitudes in Electrodermal Activity

Improved Bayesian Analysis of Metapopulation Data With an Application to a Tree Frog Metapopulation

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