Problems with the Control Variable Approach in Achieving Unbiased Estimates in Nonlinear Models in the Presence of Many Instruments

2021 ◽  
Author(s):  
Jinyong Hahn ◽  
Jerry Hausman
Keyword(s):  
Nonlinear Models ◽  
Control Variable ◽  
Variable Approach ◽  
Many Instruments ◽  
Unbiased Estimates

scholarly journals SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES

2015 ◽  
Vol 32 (5) ◽  
pp. 1140-1177 ◽  
Author(s):  
Enno Mammen ◽  
Christoph Rothe ◽  
Melanie Schienle
Keyword(s):  
Nonlinear Models ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Control Variable ◽  
Semiparametric Estimation ◽  
Nuisance Parameters ◽  
Infinite Dimensional ◽  
Asymptotically Normal ◽  
Endogenous Covariates ◽  
Nonstandard Problem

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-nconsistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.

scholarly journals The Development of a Hybrid EnKF-3DVAR Algorithm for Storm-Scale Data Assimilation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jidong Gao ◽  
Ming Xue ◽  
David J. Stensrud
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Radar Data ◽  
Ensemble Forecasts ◽  
Advanced Regional Prediction System ◽  
Error Covariance ◽  
Variable Approach ◽  
Regional Prediction ◽  
Rms Errors

A hybrid 3DVAR-EnKF data assimilation algorithm is developed based on 3DVAR and ensemble Kalman filter (EnKF) programs within the Advanced Regional Prediction System (ARPS). The hybrid algorithm uses the extended alpha control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The hybrid variational analysis is performed using an equal weighting of static and flow-dependent error covariance as derived from ensemble forecasts. The method is first applied to the assimilation of simulated radar data for a supercell storm. Results obtained using 3DVAR (with static covariance entirely), hybrid 3DVAR-EnKF, and the EnKF are compared. When data from a single radar are used, the EnKF method provides the best results for the model dynamic variables, while the hybrid method provides the best results for hydrometeor related variables in term of rms errors. Although storm structures can be established reasonably well using 3DVAR, the rms errors are generally worse than seen from the other two methods. With two radars, the results from 3DVAR are closer to those from EnKF. Our tests indicate that the hybrid scheme can reduce the storm spin-up time because it fits the observations, especially the reflectivity observations, better than the EnKF and the 3DVAR at the beginning of the assimilation cycles.

scholarly journals Some Observing System Simulation Experiments with a Hybrid 3DEnVAR System for Storm-Scale Radar Data Assimilation

2014 ◽  
Vol 142 (9) ◽  
pp. 3326-3346 ◽  
Author(s):  
Jidong Gao ◽  
David J. Stensrud
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Simulated Data ◽  
Variational Data Assimilation ◽  
Sampling Errors ◽  
Advanced Regional Prediction System ◽  
Sensitivity Experiments ◽  
Variable Approach ◽  
Regional Prediction

A hybrid three-dimensional ensemble–variational data assimilation (3DEnVAR) algorithm is developed based on the 3D variational data assimilation (3DVAR) and ensemble Kalman filter (EnKF) programs with the Advanced Regional Prediction System (ARPS). The method uses the extended control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The method is applied to the assimilation of simulated data from two radars for a supercell storm. Some sensitivity experiments are performed to answer questions about how flow-dependent covariance estimated from the forecast ensemble can be best used in the hybrid 3DEnVAR scheme. When the ensemble size is relatively small (with 5 or 10 ensemble members), it is found that experiments with a weaker weighting value for the ensemble covariance leads to better analysis results. Even when severe sampling errors exist, introducing ensemble-estimated covariances into the variational method still benefits the analysis. For reasonably large ensemble sizes (50–100 members), a stronger relative weighting (>0.8) for the ensemble covariance leads to better analyses from the hybrid 3DEnVAR. In addition, the sensitivity experiments also indicate that the best results are obtained when the number of the augmented control variables is a function of three spatial dimensions and ensemble members, and is the same for all analysis variables.

OPTIMAL CONTROL OF CRYSTALLIZATION PROCESSES

2006 ◽  
Vol 16 (12) ◽  
pp. 2029-2045 ◽  
Author(s):  
THOMAS GÖTZ ◽  
RENE PINNAU ◽  
JENS STRUCKMEIER
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Control Variable ◽  
Adjoint System ◽  
Uniqueness Of Solutions ◽  
Cost Functional ◽  
Variable Approach ◽  
And Performance ◽  
The Cost ◽  
Final Degree

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non-isothermal Avrami–Kolmogorov model and the temperature at the boundary of the domain serves as control variable. The cost functional takes into account the spatial variation of the crystallinity and the final degree of crystallization. This results in a boundary control problem for a parabolic equation coupled with two ordinary differential equations, which is treated by an adjoint variable approach. We prove the existence and uniqueness of solutions to the state system as well as the existence of a minimizer for the cost functional under consideration. The adjoint system is derived and we use a steepest descent algorithm to solve the problem numerically. Numerical simulations illustrate the applicability and performance of the optimization algorithm.

Accuracy and bias on the estimation of aboveground biomass in the woody vegetation of the Sonoran Desert

Botany ◽  
2011 ◽  
Vol 89 (9) ◽  
pp. 625-633 ◽  
Author(s):  
Alberto Búrquez ◽  
Angelina Martínez-Yrízar
Keyword(s):  
Aboveground Biomass ◽  
Sonoran Desert ◽  
Nonlinear Models ◽  
Canopy Cover ◽  
Allometric Equations ◽  
Ratio Estimator ◽  
Correction Factors ◽  
Power Functions ◽  
Unbiased Estimates ◽  
True Values

We developed allometric regressions for predicting aboveground biomass (AGB) in the Sonoran Desert. Information on canopy cover and height was collected and used to predict AGB from plant dimensions in twenty 25 m2plots that were also fully harvested. The comparison of these two methods showed that allometric equations without correction for bias led to gross AGB underestimation (four times lower than the true values for uncorrected logarithmic allometric equations). Among the tested correction factors, the ratio estimator highly reduced bias and increased accuracy. Validation of allometric estimates with whole-plot harvesting defined the best equation and the least biased correction factor. However, simple nonlinear power functions also gave accurate and unbiased estimates of AGB. We recommend the use of nonlinear models in lieu of traditional logarithm-transformed models. Correction for bias and field verification should be considered in allometric regressions used to predict AGB. In the absence of validation by direct biomass measurements, allometric predictions derived from linearization of ln-transformed data should be taken with care.

High-purity Ge x-ray detectors: Sensitivity factors and usefulness

1990 ◽  
Vol 48 (2) ◽  
pp. 548-548
Author(s):  
E. B. Steel
Keyword(s):  
High Purity ◽  
High Energy ◽  
Quantitative Chemical Analysis ◽  
Detector Performance ◽  
X Ray ◽  
Detector Sensitivity ◽  
Specimen Holder ◽  
Many Instruments ◽  
Charge Resolution ◽  
Sensitivity Factors

High Purity Germanium (HPGe) x-ray detectors are now commercially available for the analytical electron microscope (AEM). The detectors have superior efficiency at high x-ray energies and superior resolution compared to traditional lithium-drifted silicon [Si(Li)] detectors. However, just as for the Si(Li), the use of the HPGe detectors requires the determination of sensitivity factors for the quantitative chemical analysis of specimens in the AEM. Detector performance, including incomplete charge, resolution, and durability has been compared to a first generation detector. Sensitivity factors for many elements with atomic numbers 10 through 92 have been determined at 100, 200, and 300 keV. This data is compared to Si(Li) detector sensitivity factors.The overall sensitivity and utility of high energy K-lines are reviewed and discussed. Many instruments have one or more high energy K-line backgrounds that will affect specific analytes. One detector-instrument-specimen holder combination had a consistent Pb K-line background while another had a W K-line background.

Real-ear Masking Calibration for Portable Pure-Tone Audiometers

1984 ◽  
Vol 15 (4) ◽  
pp. 289-294
Author(s):  
Martin S. Robinette ◽  
Robert H. Brey
Keyword(s):  
Pure Tone ◽  
Broad Band ◽  
Resistive Network ◽  
Many Instruments

A transformer mixing network is described which allows the calibration of broad-band masking for portable audiometers that lack a built-in mixing network. For many instruments the transformer network is preferable to the resistive network previously published.

Distinguishing Adequate Versus Inadequate Cancer Health Literacy Levels: A Discrete Latent Variable Approach

2013 ◽  
Author(s):  
Levent Dumenci ◽  
Robin Matsuyama ◽  
Robert Perera ◽  
Laura Kuhn ◽  
Laura Siminoff
Keyword(s):  
Health Literacy ◽  
Latent Variable ◽  
Variable Approach ◽  
Latent Variable Approach
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