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Introduction
Published in Bradley Efron, R.J. Tibshirani, An Introduction to the Bootstrap, 1994
Bradley Efron, R.J. Tibshirani
The delta method is a special technique for variance estimation that is applicable to statistics that are functions of observed averages. Suppose that we can write θˆX1,X2,…Xn=rQ‾1,Q‾2,…Q‾A
Optimization of Food Processes Using Mixture Experiments
Published in Surajbhan Sevda, Anoop Singh, Mathematical and Statistical Applications in Food Engineering, 2020
Daniel Granato, Verônica Calado, Edmilson Rodrigues Pinto
Statistical modeling of variance in mixture experiments with noise variables has been considered in Steiner and Hamada, 1997, who proposed a combined mixture-process-noise variable model. They built and solved an optimization problem to minimize a quadratic loss function, taking into account both the mean and variance of response. Another approach to modeling the variance is due to Goldfarb et al., 2003 using the delta method, which employs a first-order Taylor series approximation of the regression model at a vector of noise variables. The delta method is a well-known technique, based on Taylor series expansions, for finding approximations to the mean and variance of functions of random variables.
E
Published in Carl W. Hall, Laws and Models, 2018
where h = a measure of precision in making measurements assuming that the mean is zero. Keywords: error, frequency, observation, random, statistics GAUSS, Karl F., 1777-1855, German mathematician Sources: Freiberger, W. F. 1960; Gillispie, C. C. 1996; Hall, C. W. 1977. See also ERROR FUNCTION; LARGE NUMBERS; NORMAL DISTRIBUTION; STANDARD ERROR ERRORS, LAW OF; ALSO CENTRAL LIMIT THEOREM The average of a large number of independent and identically distributed random variables is approximately normally distributed. A scatter of a set of readings obeys the theory of probability as incorporated by the standard deviation. Keywords: average, distributed, independent, normally, random Sources: Bothamley, J. 1993; Freiberger, W. F. 1960; Honig, J. M. 1953; Morris, C. G. 1992; Gillispie, C. C. 1990; Whitehead, A. N. 1949. 1954. See also CENTRAL LIMIT THEOREM; NORMAL DISTRIBUTION; PROBABILITY; STANDARD ERROR ERRORS, LAWS OF I. Development of concept by numerous people, depending on application II. Gaussian distribution or normal distribution III. Non-Gaussian distribution Source: Kotz, S. and Johnson, N. 1982. 1988. ERRORS, PROPAGATION LAW OF The variance formula obtained by the delta method is called the law of propagation of errors. ^ ^ For large sample sizes, the properties of an estimate g ( ) of g() where ( ) is an estimator of () often may be studied using the delta method. The delta method involves functions g and estimators (0) and expansion of g(0) in a Taylor series (see reference). Keywords: delta, estimate, propagation, properties Source: Lerner, R. G. and Trigg, G. L. 1981. 1991. ESTERIFICATION, LAW OF--SEE MEYER (VICTOR) ETTINGSHAUSEN EFFECT OR LAW (1887) (OR VON ETTINGSHAUSEN) An electric current flowing across the lines of flux of a magnetic field produces an electromotive force which is at right angles to both the primary current and the magnetic field, and a temperature gradient is produced opposite in direction to the Hall electromotive force. Keywords: current, electricity, Hall, magnetic, temperature
Climate change risks and vulnerabilities during mining exploration, operations, and reclamation: A regional approach for the mining sector in Québec, Canada
Published in CIM Journal, 2022
É. Bresson, B. Bussière, T. Pabst, I. Demers, P. Charron, P. Roy
Global climate models have coarse horizontal resolutions (approximately 200 km) and different numerical parametrizations. Gridded daily observations from Natural Resources Canada (NRCan; Hutchinson et al., 2009) were used to conduct a bias correction on the climate indices over the historical and future periods to improve coherence with local historical climate. First, global climate model data were interpolated over NRCan daily observations grid. Over the common period (1981–2010), the climatological difference between the NRCan observations and the simulation represents the bias of the index. The index bias was then subtracted (delta method) from the simulated index over the historical and future periods. The delta method adjusts the mean, but not the variance of the index distributions. Finally, results were aggregated over each region of interest.
Investigation of stochastic variation of parameters for a macroscopic traffic model
Published in Journal of Intelligent Transportation Systems, 2018
Elvira Thonhofer, Stefan Jakubek
As an alternative to the analytic computation one can employ the delta method (Cramér, 2016; Greene, 2003). The delta method is an approach for computing the variance of a function of maximum likelihood estimates. It is applied to functions that are too complicated for the analytic computation of variance (and mean). The function of interest is expanded into a Taylor series, which is truncated after the first-order term. Thereby errors of order 2 with respect to are introduced.