scholarly journals Weighted Least Squares Estimates of the Magnetotelluric Transfer Functions from Nonstationary Data

1982 ◽  
Author(s):  
John A. Stodt
Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 95
Author(s):  
Pontus Söderbäck ◽  
Jörgen Blomvall ◽  
Martin Singull

Liquid financial markets, such as the options market of the S&P 500 index, create vast amounts of data every day, i.e., so-called intraday data. However, this highly granular data is often reduced to single-time when used to estimate financial quantities. This under-utilization of the data may reduce the quality of the estimates. In this paper, we study the impacts on estimation quality when using intraday data to estimate dividends. The methodology is based on earlier linear regression (ordinary least squares) estimates, which have been adapted to intraday data. Further, the method is also generalized in two aspects. First, the dividends are expressed as present values of future dividends rather than dividend yields. Second, to account for heteroscedasticity, the estimation methodology was formulated as a weighted least squares, where the weights are determined from the market data. This method is compared with a traditional method on out-of-sample S&P 500 European options market data. The results show that estimations based on intraday data have, with statistical significance, a higher quality than the corresponding single-times estimates. Additionally, the two generalizations of the methodology are shown to improve the estimation quality further.


1986 ◽  
Vol 16 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Edwin J. Green ◽  
William E. Strawderman

A Stein-rule estimator, which shrinks least squares estimates of regression parameters toward their weighted average, was employed to estimate the coefficient in the constant form factor volume equation for 18 species simultaneously. The Stein-rule procedure was applied to ordinary least squares estimates and weighted least squares estimates. Simulation tests on independent validation data sets revealed that the Stein-rule estimates were biased, but predicted better than the corresponding least squares estimates. The Stein-rule procedures also yielded lower estimated mean square errors for the volume equation coefficient than the corresponding least squares procedure. Different methods of withdrawing sample data from the total sample available for each species revealed that the superiority of Stein-rule procedures over least squares decreased as the sample size increased and that the Stein-rule procedures were robust to unequal sample sizes, at least on the scale studied here.


Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. E237-E247 ◽  
Author(s):  
Rita Streich ◽  
Michael Becken ◽  
Oliver Ritter

Whereas robust processing techniques are routinely used for estimating high-quality magnetotelluric (MT) transfer functions, such techniques are not commonly applied for controlled-source electromagnetic (CSEM) processing, although CSEM and MT data suffer from similar noise. We implemented a new CSEM processing scheme that combines CSEM-specific preprocessing with statistically robust least-squares stacking to extract interpretable ground responses from very noisy onshore CSEM data. We applied the robust processing to signals from a new CSEM transmitter that was equipped with three grounded electrodes and allowed us to generate signals at multiple source polarizations with relatively little field effort. For this transmitter setup, we formulated a bivariate relation between the source currents injected through any two of the three source electrodes and the recorded electromagnetic field components. The resulting weighted least-squares system of equations from which we determined ground responses allowed us to jointly process data from multiple polarizations. Using several polarizations resulted in more stable response estimates than can be obtained from standard configurations with two distinct source dipole orientations. Exploiting dependencies between the three basic response functions that we obtain allows consistency checking and demonstrates the stability of our robust processing scheme. From the basic responses, data at arbitrary source polarizations can be synthesized, which may be useful for optimizing target illumination. We tested the benefits of robust CSEM processing using examples of data recorded across the [Formula: see text] storage test site at Ketzin, Germany, in an area heavily affected by various sources of strong cultural noise, including impressed-current cathodic protection systems, wind power plants, and major power lines.


Sign in / Sign up

Export Citation Format

Share Document