scholarly journals Complete subset averaging with many instruments

2020 ◽  
Author(s):  
Seojeong Lee ◽  
Youngki Shin
Keyword(s):  
Demand Function ◽  
Simulation Experiment ◽  
Mean Squared Error ◽  
Asymptotic Optimality ◽  
Weighted Average ◽  
Subset Size ◽  
Extensive Simulation ◽  
Squared Error ◽  
Many Instruments ◽  
Class Of Estimators

Summary We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalise the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry et al. (1995) and find that the CSA-2SLS estimate is better supported by economic theory than are the alternative estimates.

Linear Prediction of a True Score From a Direct Estimate and Several Derived Estimates

2007 ◽  
Vol 32 (1) ◽  
pp. 6-23 ◽  
Author(s):  
Shelby J. Haberman ◽  
Jiahe Qian
Keyword(s):  
Linear Prediction ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Statistical Prediction ◽  
True Score ◽  
Direct Estimate ◽  
Linear Predictor ◽  
Squared Error ◽  
Best Linear Predictor ◽  
Prediction Problems

Statistical prediction problems often involve both a direct estimate of a true score and covariates of this true score. Given the criterion of mean squared error, this study determines the best linear predictor of the true score given the direct estimate and the covariates. Results yield an extension of Kelley’s formula for estimation of the true score to cases in which covariates are present. The best linear predictor is a weighted average of the direct estimate and of the linear regression of the direct estimate onto the covariates. The weights depend on the reliability of the direct estimate and on the multiple correlation of the true score with the covariates. One application of the best linear predictor is to use essay features provided by computer analysis and an observed holistic score of an essay provided by a human rater to approximate the true score corresponding to the holistic score.

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals A generalized exponential-type estimator for population mean using auxiliary attributes

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0246947
Author(s):  
Sohail Ahmad ◽  
Muhammad Arslan ◽  
Aamna Khan ◽  
Javid Shabbir
Keyword(s):  
Exponential Type ◽  
Random Sampling ◽  
Finite Population ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Stratified Random Sampling ◽  
Population Mean ◽  
First Order ◽  
Squared Error ◽  
Class Of Estimators

In this paper, we propose a generalized class of exponential type estimators for estimating the finite population mean using two auxiliary attributes under simple random sampling and stratified random sampling. The bias and mean squared error (MSE) of the proposed class of estimators are derived up to first order of approximation. Both empirical study and theoretical comparisons are discussed. Four populations are used to support the theoretical findings. It is observed that the proposed class of estimators perform better as compared to all other considered estimator in simple and stratified random sampling.

scholarly journals A method for colocating satellite <i>X</i><sub>CO<sub>2</sub></sub> data to ground-based data and its application to ACOS-GOSAT and TCCON

2014 ◽  
Vol 7 (8) ◽  
pp. 2631-2644 ◽  
Author(s):  
H. Nguyen ◽  
G. Osterman ◽  
D. Wunch ◽  
C. O'Dell ◽  
L. Mandrake ◽  
...  
Keyword(s):  
Mean Squared Error ◽  
Weighted Average ◽  
Satellite Observations ◽  
Total Carbon ◽  
Satellite Measurements ◽  
Temporal Window ◽  
Squared Error ◽  
Scanning Imaging ◽  
Total Column ◽  
Absorption Spectrometer

Abstract. Satellite measurements are often compared with higher-precision ground-based measurements as part of validation efforts. The satellite soundings are rarely perfectly coincident in space and time with the ground-based measurements, so a colocation methodology is needed to aggregate "nearby" soundings into what the instrument would have seen at the location and time of interest. We are particularly interested in validation efforts for satellite-retrieved total column carbon dioxide (XCO2), where XCO2 data from Greenhouse Gas Observing Satellite (GOSAT) retrievals (ACOS, NIES, RemoteC, PPDF, etc.) or SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) are often colocated and compared to ground-based column XCO2 measurement from Total Carbon Column Observing Network (TCCON). Current colocation methodologies for comparing satellite measurements of total column dry-air mole fractions of CO2 (XCO2) with ground-based measurements typically involve locating and averaging the satellite measurements within a latitudinal, longitudinal, and temporal window. We examine a geostatistical colocation methodology that takes a weighted average of satellite observations depending on the "distance" of each observation from a ground-based location of interest. The "distance" function that we use is a modified Euclidian distance with respect to latitude, longitude, time, and midtropospheric temperature at 700 hPa. We apply this methodology to XCO2 retrieved from GOSAT spectra by the ACOS team, cross-validate the results to TCCON XCO2 ground-based data, and present some comparisons between our methodology and standard existing colocation methods showing that, in general, geostatistical colocation produces smaller mean-squared error.

scholarly journals Average Derivative Estimation from Biased Data

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Christophe Chesneau ◽  
Maher Kachour ◽  
Fabien Navarro
Keyword(s):  
Rate Of Convergence ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Derivative Estimation ◽  
Squared Error ◽  
The Mean ◽  
Average Derivative Estimation ◽  
Average Derivative

We investigate the estimation of the density-weighted average derivative from biased data. An estimator integrating a plug-in approach and wavelet projections is constructed. We prove that it attains the parametric rate of convergence 1/n under the mean squared error.

scholarly journals A General Class of Dual to Ratio Estimator

2020 ◽  
pp. 421-431
Author(s):  
Housila Prasad Singh ◽  
Pragati Nigam
Keyword(s):  
General Class ◽  
Mean Squared Error ◽  
Auxiliary Information ◽  
Ratio Estimator ◽  
Sample Surveys ◽  
Sample Mean ◽  
Population Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
Ratio Estimators

In this paper we have considered the problem of estimating the population mean using auxiliary information in sample surveys. A class of dual to ratio estimators has been defined. Exact expressions for bias and mean squared error of the suggested class of dual to ratio estimator have been obtained. In particular, properties of some members of the proposed class of dual to ratio estimators have been discussed. It has been shown that the proposed class of estimators is more efficient than the sample mean, ratio estimator, dual to ratio estimator and some members of the suggested class of estimators in some realistic conditions. Some numerical illustrations are given in support of the present study.

scholarly journals Estimation of Population Median under Robust Measures of an Auxiliary Variable

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Irfan ◽  
Maria Javed ◽  
Sandile C. Shongwe ◽  
Muhammad Zohaib ◽  
Sajjad Haider Bhatti
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Real Life ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
First Order ◽  
Mathematical Properties ◽  
Squared Error ◽  
Class Of Estimators ◽  
Robust Measures

In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

scholarly journals A method for colocating satellite <i>X</i><sub>CO<sub>2</sub></sub> data to ground-based data and its application to ACOS-GOSAT and TCCON

2014 ◽  
Vol 7 (2) ◽  
pp. 1495-1533
Author(s):  
H. Nguyen ◽  
G. Osterman ◽  
D. Wunch ◽  
C. O'Dell ◽  
L. Mandrake ◽  
...  
Keyword(s):  
Greenhouse Gas ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Total Carbon ◽  
Tropospheric Temperature ◽  
Satellite Measurements ◽  
Temporal Window ◽  
Squared Error ◽  
Scanning Imaging ◽  
Total Column

Abstract. Satellite measurements are often compared with higher-precision ground-based measurements as part of validation efforts. The satellite soundings are rarely perfectly coincident in space and time with the ground-based measurements, so a colocation methodology is needed to aggregate "nearby" soundings into what the instrument would have seen at the location and time of interest. We are particularly interested in validation efforts for satellite-retrieved total column carbon dioxide (XCO2), where XCO2 data from Greenhouse Gas Observing Satellite (GOSAT) retrievals (ACOS, NIES, RemoteC, PPDF, etc.) or SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCHIACHY) are often colocated and compared to ground-based column XCO2 measurement from Total Carbon Column Observing Network (TCCON). Current colocation methodologies for comparing satellite measurements of total column dry-air mole fractions of CO2 (XCO2) with ground-based measurements typically involve locating and averaging the satellite measurements within some latitudinal, longitudinal, and temporal window. We examine a geostatistical colocation methodology that takes a weighted average of satellite observations depending on the "distance" of each observation from a ground-based location of interest. The "distance" function that we use is a modified Euclidian distance with respect to latitude, longitude, time, and mid-tropospheric temperature at 700 hPa. We apply this methodology to XCO2 retrieved from Greenhouse Gas Observing Satellite (GOSAT) spectra by the ACOS team, cross-validate the results to TCCON XCO2 ground-based data, and present some comparison between our methodology and standard existing colocation methods showing that in general geostatistical colocation produces smaller mean-squared error.

scholarly journals Efficient Method of Estimating the Finite Population Mean Based on Two Auxiliary Variables in the Presence of Non-Response Under Stratified Sampling

2021 ◽  
Author(s):  
Housila P. Singh ◽  
Pragati Nigam
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Variables ◽  
Optimum Conditions ◽  
Study Variable ◽  
Numerical Illustration ◽  
Population Mean ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Class Of Estimators ◽  
Better Than

This article addresses the problem of estimating the population mean using information on two auxiliary variables in presence of non-response on study variable only under stratified random sampling. A class of estimators has been defined. We have derived the bias and mean squared error up to first order of approximation. Optimum conditions are obtained in which the suggested class of estimators has minimum mean squared error. In addition to Chaudhury et al. (2009) estimator, many estimators can be identified as a member of the suggested class of estimators. It has been shown that the suggested class of estimators is better than the Chaudhury et al. (2009) estimator and other estimators. Results of the present study are supported through numerical illustration.

scholarly journals Some Improved Estimators in Double Sampling Using two Auxiliary Variables

2015 ◽  
Vol 19 (2) ◽  
pp. 97
Author(s):  
Mohammad S. Ahmed
Keyword(s):  
Mean Squared Error ◽  
Double Sampling ◽  
Auxiliary Variables ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Series Expression ◽  
Optimum Estimator ◽  
Class Of Estimators ◽  
Improved Estimators ◽  
Taylor’S Series

Dash and Mishra [1] suggested an improved class of estimators without defining the optimum estimator. However, they gave the wrong Taylor’s series expression of their class of estimator and their minimum mean squared error expressions are also incorrect. Here we show that Ahmed et al.’s [2] class of chain estimators is more efficient than Dash and Mishra’s [1], with minimum mean squared error.  

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