Generalized Regression Estimator Research Articles

Review of how the generalized regression estimators contribute to estimating the financial and economic data with missing observations under unequal probability sampling

PurposeKnowing financial and economic information beforehand benefits in planning and developing policies for every country especially for a developing country like Thailand and for other Asian countries. Unfortunately, missing data or non-response plays an essential role in many areas of studies including finance and economics. Eradication of missing data in a proper way before further analysis can gain remarkable outcomes and can be effective for planning policies. This review on the generalized regression estimators for population total can be applied to financial, economic and other data when missing data are present.Design/methodology/approachThe generalized regression estimators for estimating population total, including the variance estimators under unequal probability sampling without replacement with missing data are explored under the reverse framework. Applications to financial and economic data in Thailand are also reviewed.FindingsThe review of literatures related to the proposed estimator shows the best performance, giving smaller variances in all scenarios.Originality/valueThe generalized regression estimators can assist in estimating financial and economic data that contain missing values with different missing mechanisms and can be used in other applications which help gain more superior estimators.

Poisson-modification of the Quasi Lindley optimal generalized regression estimator

In this paper, we propose an optimal generalized regression estimator based on the sample information for the Poisson-Modification of the Quasi Lindley (PMQL) regression model namely the PMQL optimal generalized regression estimator. Asymptotic properties of the proposed estimator are obtained. Further, the conditions of superiority over some other regression coefficient estimators for the PMQL regression model are also derived based on the mean square error criterion. In order to compare the performance of the proposed estimator over some other PMQL regression coefficient estimators in the scalar mean square error sense, a Monte Carlo simulation study is designed and results are discussed. Finally, a simulated data example and a real-world example are taken to show the potentiality of the new regression model based on the proposed estimator and show the consistency of the theoretical and simulation results, respectively.

Simulation analysis of non-respondent information in context of small domain

In the real-world, there are various situations when all units are not accessible of the respondent called unit non-response. The effect of unit non-response is a tricky matter for estimating the total number of unit. The present work highlights the interest about subpopulations (domains) in two affairs: i. if domains total of the supportive information is accessible ii. if domains total of the supportive variable does not access. The government needs to be introducing the actual facilities in these small domains. The supportive information is used to find out the estimate of the non respondent information and to apply this information for desired domains. Sometimes, it has been found that the accessible auxiliary variable for the domains might be positive shape. Therefore, it develops an appropriate model that has positive skewness. The present context highlighted the indirect method using a power-based estimation with calibration approach. By combining power based estimation and calibration technique, it is possible to obtain more accurate estimates for intended small domains. Even the supportive information is positively biased. This approach helps us in mitigating the effect of non-respondent and improving the overall reliability of the estimators. The simulation was conducted for different sizes 70 and 90 when nonresponse variable in the study variable. The results show that investigated power-based estimate provides better option over relevant exponential, ratio, and generalized regression estimators for intended domains.

Generalized regression estimators with concave penalties and a comparison to lasso type estimators

Generalized regression estimators with concave penalties and a comparison to lasso type estimators

Jackknife Bias-Corrected Generalized Regression Estimator in Survey Sampling

Abstract The generalized regression (GREG) estimator is a well-known procedure for using auxiliary data to estimate means or totals using a sample selected from a finite population. The GREG estimator is motivated by an assumed linear superpopulation model and it is known to be asymptotically unbiased regardless of whether the model is correctly specified or not. When the sample size is small and/or when the linear model does not fit the sample data well, the GREG estimator may have nonnegligible bias. In this article, we use the jackknife procedure to correct the bias of the GREG. We evaluate, both theoretically and by simulation, the performance of the jackknife bias-corrected regression estimator (GREG-JK) under unistage sampling without replacement with unequal probabilities. A jackknife mean squared error (MSE) estimator is proposed that naturally includes a finite population correction, which is usually absent in the standard jackknife methods for variance estimation. A simulation study shows that the empirical bias of GREG-JK is negligible for all sample sizes and generated populations. Furthermore, the proposed jackknife MSE estimator demonstrates improvements over the customary estimator.

New Generalized Regression Estimators Using a Ratio Method and Its Variance Estimation for Unequal Probability Sampling without Replacement in the Presence of Nonresponse

One of the most important problems for planning in economics is that reliable data can be difficult to obtain either because it has not been recorded or because of nonresponse in surveys. This paper is aimed at proposing new generalized regression estimators using the ratio method of estimation for estimating population mean and population total and also variance estimators of the proposed generalized regression estimators in the presence of uniform nonresponse of a study variable. We show in theory that the proposed estimators are almost unbiased under unequal probability sampling without replacement when nonresponse occurs in the study. In the simulation studies, the performances of the proposed estimators were better when compared to the existing ones in terms of minimum relative bias and relative root mean square error. In an application to Thai maize in Thailand with 2019 data, we can see that the proposed estimators gave smaller variance estimates when compared to the existing estimators

Analysis on the Development Strategy of Private Education Based on Data Mining Algorithm

In order to improve the development effect of private education, this paper analyzes the current situation of private education combined with the data mining algorithm and explores the problems existing in the development of private education. Moreover, this paper combines the semi-parametric product estimation method with parameter estimation and applies the estimation method to model-assisted sampling estimation. This work enhances the estimate accuracy of the sample estimation and increases the field of application of the model while enhancing the classic generalized regression estimation. It also modifies the estimation accuracy on the basis of the linear assumption. The experimental study reveals that the data mining algorithm-based analysis approach for private education development provided in this work has a certain impact, and the development strategy of private education is assessed on this premise.

Analysis of Influencing Factors of Social Public Management Score Based on Augmented Regression Model

To improve the analysis effect of the factors influencing the score of social public management, this paper combines the enhanced regression model to analyze the factors affecting the score of social public management and constructs a factor analysis model through an intelligent algorithm. Moreover, this paper uses numerical simulation to verify that when the parameters estimated by SEM are linear functions and the relationship between the research variables and auxiliary variables is nonlinear, the estimation effect of SEM estimators is better than that of traditional generalized regression estimators. In addition, this paper proposes a public service channel management model through the measurement and analysis of channel mode public service feature matching, channel type public service feature matching, and channel type and channel mode public service feature matching. Finally, this paper combines the simulation research to verify the effectiveness of the method in this paper.

Small Area Estimates for National Applications: A Database to Dashboard Strategy Using FIESTA

This paper demonstrates a process for translating a database of forest measurements to interactive dashboards through which users can access statistically defensible estimates and analyses anywhere in the conterminous US. It taps the extensive Forest Inventory and Analysis (FIA) plot network along with national remotely sensed data layers to produce estimates using widely accepted model-assisted and small area estimation methodologies. It leverages a decade’s worth of statistical and computational research on FIA’s flexible estimation engine, FIESTA, and provides a vehicle through which scientists and analysts can share their own tools and analytical processes. This project illustrates one pathway to moving statistical research into operational inventory processes, and makes many model-assisted and small area estimators accessible to the FIA community. To demonstrate the process, continental United States (CONUS)-wide model-assisted and small area estimates are produced for ecosubsections, counties, and level 5 watersheds (HUC 10) and made publicly available through R Shiny dashboards. Target parameters include biomass, basal area, board foot volume, proportion of forest land, cubic foot volume, and live trees per acre. Estimators demonstrated here include: the simplest direct estimator (Horvitz–Thompson), model-assisted estimators (post-stratified, generalized regression estimator, and modified generalized regression estimators), and small area estimators (empirical best linear unbiased predictors and hierarchical Bayes both at the area- and unit-level). Auxiliary data considered in the model-assisted and small area estimators included maps of tree canopy, tree classification, and climatic variables. Estimates for small domain sets were generated nationally within a few hours. Exploring results across estimators and target variables revealed the progressive gains in precision using (in order of least gain to highest gain) Horvitz–Thompson, post-stratification, modified generalized regression estimators, generalized regression estimators, area-level small area models, and unit-level small area models. Substantive gains are realized by expanding model-assisted estimators beyond post-stratification, allowing FIA to continue to take advantage of design-based inference in many cases. Caution is warranted in the use of unit-level small area models due to model mis-specification. The dataset of estimates available through the dashboards provides the opportunity for others to compare estimators and explore precision expectations over specific domains and geographic regions. The dashboards also provide a forum for future development and analyses.

Examining k-Nearest Neighbor Small Area Estimation Across Scales Using National Forest Inventory Data

National forest inventories (NFI), such as the one conducted by the United States Forest Service Forest Inventory and Analysis (FIA) program, provide valuable information regarding the status of forests at regional to national scales. However, forest managers often need information at stand to landscape scales. Given various small area estimation (SAE) approaches, including design-based and model-based estimation, it may not be clear which is most appropriate for the user’s application. In this study, our objective was to assess the uncertainty in tree aboveground live carbon (ALC) estimates for differing modes of SAE across multiple scales to provide guidance for appropriate scales of application. We calculated means and variances for ALC with design-based (Horvitz-Thompson), model-assisted (generalized regression), and model-based (k-nearest neighbor synthetic) estimators for estimation units over a range of sizes for 30 subregions in California, United States. For larger areas (10,000–64,800 ha), relative efficiencies greater than one indicated that the generalized regression estimator (GREG) generated estimates with less error than the Horvitz-Thompson estimator (HT), while the bias-adjusted synthetic estimator relative efficiency compared to either the Horvitz-Thompson or model-assisted estimators exceeded one for areas 25,000 ha and smaller. Variance estimates from the unadjusted synthetic estimator underestimated the total error, because the estimator ignores bias and thus only addresses model variance. Across scales (250–64,800 ha, 0–27 plots per area of interest), 93% of the variation in the synthetic estimator’s relative standard error was explained by forest area, forest dominance, and regional variation in forest landscapes. Our results support model-assisted estimation use except for small areas where few plots (<10 in the current study) are available for generating estimates in spite of biases in estimates. However, users should exercise caution when interpreting model-based estimates of error as they may not account for model mis-specification, and thus induced bias. This research explored multiple scales of application for SAE procedures applied to NFI data regarding carbon pools, potentially supporting a multi-scale approach to forest monitoring. Our results guides users in developing defensible estimates of carbon pools, particularly as it relates to the limits of inference at a variety of spatial scales.

Generalized regression estimation for continuous time processes with values in functional spaces

We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination'' (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the convergence of the conditional distribution function as well as conditional quantiles. Note that a parametric rate of convergence in probability is reached while working with a naive kernel.

GREGORY: A Modified Generalized Regression Estimator Approach to Estimating Forest Attributes in the Interior Western US

The national forest inventory within the US has been experiencing a greater need to estimate forest attributes over smaller geographic areas than the inventory was originally designed for. Producing reliable estimates for these areas may require the use of estimation methods beyond post-stratification. Staying within the dominant design-based paradigm, this research explores how model-assisted estimation is impacted by leveraging data outside the area of interest. In particular, we compare the performance of the post-stratified estimator, the generalized regression estimator (GREG), and a modified GREG. Typically the assisting model of the modified GREG is fit over a sample comprising all of the areas of interest. Here we introduce a modified GREG, denoted as GREGORY, which gives the practitioner a high degree of flexibility in selecting the sample subset for constructing the assisting model. We use these estimators to produce county level estimates of the mean of four forest attributes in the Interior Western US. Comparing the relative efficiencies of the estimators, we find that the more complex estimators, GREG and GREGORY, generally improve the precision of the estimates, especially in regions with a high degree of forested land. When using all the data from a 10-year measurement, fitting the model over a larger region does not lead to efficiency gains. To explore the impact of smaller sample sizes, we conduct a simulation study and find that as the sampling intensity decreases, the GREGORY tends to produce more efficient estimates than the GREG, and its variance estimator exhibits less negative bias. The GREG and GREGORY can easily be computed and compared using a new R package, gregRy, available on CRAN.

Sampling-Based Approaches to Estimating Two-Dimensional Large Wood Area from UAS Imagery

Large in-stream wood (LW) is a critical component of riparian systems that increases heterogeneity of flow regimes and provides high habitat for salmonids and other fishes. We present four sampling-based methods to estimate two-dimensional LW for a 61-hectare river restoration project on the South Fork McKenzie River near Rainbow, OR (USA). We manually delineated LW area, from unoccupied aircraft systems (UAS) multispectral imagery for 40 randomly selected 51.46 m2 hexagonal plots. Seven auxiliary variables were extracted from the imagery and imagery derivatives to be incorporated in four estimators by summarizing spectral statistics for each plot including Random forest (RF) classification of segmented imagery (Cohen’s kappa = 0.75, balanced accuracy = 0.86). The four estimators were: difference estimator, simple linear regression estimator with one auxiliary variable, general regression estimator with seven auxiliary variables, and simple random sample without replacement. We assessed variance of the estimators and found that the simple random sample without replacement produced the largest estimate for LW area and widest confidence interval (17,283 m2, 95% CI 10,613 - 23,952 m2) while the generalized regression approach resulted in the smallest estimate and narrowest confidence interval (16,593 m2, 95% CI 13,054 - 20,133 m2). These methods facilitate efficient estimates of critical habitat components, that are especially suited to efforts that seek to quantify large amounts of these components through time. When combined with traditional sampling methods, classified imagery acquired via UAS promises to enhance the temporal resolution of the data products associated with restoration efforts while minimizing the necessity for potentially hazardous field work.

Some Model Assisted Estimators Using Functional Form Calibration Approach

The Model assisted estimators are approximately design unbiased, consistent and provides robustness in the case of large sample sizes. The model assisted estimators result in reduction of the design variance if underlying model reasonably defines the regression relationship. If the model is misspecified, then model assisted estimators might result in an increase of the design variance but remain approximately design unbiased and show robustness against model-misspecification. The well-known model assisted estimators, generalized regression estimators are members of a larger class of calibration estimators. Calibration method generates calibration weights that meet the calibration constraints and have minimum distance from the sampling design weights. By using different distance measures, classical calibration approach generates different calibration estimators but with asymptotically identical properties. The constraint of distance minimization was reduced for studying the properties of calibration estimators by proposing a simple functional form approach. The approach generates calibration weights that prove helpful to control the changes in calibration weights by using different choices of auxiliary variable’s functions. This paper is an extended work on model assisted approach by using functional form of calibration weights. Some new model assisted estimators are considered to get efficient and stabilized regression weights by introducing a control matrix. The asymptotic un-biasedness of the proposed estimators is verified and the expressions for MSE are derived in three different cases. A simulation study is done to compare and evaluate the efficiency of the proposed estimators with some existing model assisted estimators.

Moment estimation for censored quantile regression

In influential articles Powell (Journal of Econometrics 25(3):303–325, 1984; Journal of Econometrics 32(1):143–155, 1986) proposed optimization-based censored least absolute deviations estimator (CLAD) and general censored quantile regression estimator (CQR). It has been recognized, however, that this optimization-based estimator may perform poorly in finite samples (e.g., Khan and Powell, Journal of Econometrics 103(1–2):73–110, 2001; Fitzenberger, Handbook of Statistics. Elsevier, 1996; Fitzenberger and Winker, Computational Statistics & Data Analysis 52(1):88–108, 2007; Koenker, Journal of Statistical Software 27(6), 2008). In this paper we propose a moment-based censored quantile regression estimator (MCQR). While both the CQR and MCQR estimators have the same large sample properties, our simulation results suggest certain advantage of our moment-based estimator (MCQR). In addition, the empirical likelihood methods for the uncensored model (e.g., Whang 2006; Otsu, Journal of Econometrics 142(1):508–538, 2008) can readily be adapted to the censored model within our method of moment estimation framework. When both censoring and endogeneity are present, we develop an instrumental variable censored quantile regression estimator (IVCQR) by combining the insights of Chernozhukov and Hansen’s (Journal of Econometrics 132(2):491–525, 2006; Journal of Econometrics 142(1):379–398, 2008) instrumental variables quantile regression estimator (IVQR) and the MCQR. Simulation results indicate that the IVCQR estimator performs well.

Restricted calibration and weight trimming approaches for estimation of the population total in business statistics

Some adjustments are made to design weights to reduce the negative effects of non-response and out-of-scope problems. The calibration approach is a weighting process that agrees with the known population values by using auxiliary information. In this study, alternative calibration approaches and weight trimming process that can be used in large data sets with extreme weights and different correlation structures were analysed. In addition, the effect of the correlation structure of auxiliary variables on the efficiency of the calibration estimators was investigated by a simulation study. The 2017 Annual Industry and Service Statistics data were used in the simulation study and it was seen that restricted calibration estimators were more efficient than the generalized regression estimator in estimating the variables with a high variance such as turnover. Especially in small sample fractions, we recommend the application of restricted calibration estimators, as they are more efficient than the weight trimming in solving the negative and less than one weights problem encountered after the calibration process.

A new generalized regression estimator and variance estimation for unequal probability sampling without replacement for missing data

The aim of this paper is to develop a new generalized regression estimator along with a method for estimating the variance of a population total using unequal probability sampling without replacement in the presence of nonresponse. We consider under less restricted situations where response probabilities are non-uniform and a sampling fraction can be both negligible and not negligible where both circumstances are more realistic in practice under the reverse framework. Theoretical proof shows that the new estimator is an almost unbiased estimator measured under the missing at random mechanism. Simulation studies and real data are used to exhibit some properties of the proposed estimators.

A Tutorial on Model-Assisted Estimation with Application to Forest Inventory

National forest inventories in many countries combine expensive ground plot data with remotely-sensed information to improve precision in estimators of forest parameters. A simple post-stratified estimator is often the tool of choice because it has known statistical properties, is easy to implement, and is intuitive to the many users of inventory data. Because of the increased availability of remotely-sensed data with improved spatial, temporal, and thematic resolutions, there is a need to equip the inventory community with a more diverse array of statistical estimators. Focusing on generalized regression estimators, we step the reader through seven estimators including: Horvitz Thompson, ratio, post-stratification, regression, lasso, ridge, and elastic net. Using forest inventory data from Daggett county in Utah, USA as an example, we illustrate how to construct, as well as compare the relative performance of, these estimators. Augmented by simulations, we also show how the standard variance estimator suffers from greater negative bias than the bootstrap variance estimator, especially as the size of the assisting model grows. Each estimator is made readily accessible through the new R package, mase. We conclude with guidelines in the form of a decision tree on when to use which an estimator in forest inventory applications.

Generalized Regression Estimators with High-Dimensional Covariates.

Data from a large number of covariates with known population totals are frequently observed in survey studies. These auxiliary variables contain valuable information that can be incorporated into estimation of the population total of a survey variable to improve the estimation precision. We consider the generalized regression estimator formulated under the model-assisted framework in which a regression model is utilized to make use of the available covariates while the estimator still has basic design-based properties. The generalized regression estimator has been shown to improve the efficiency of the design-based Horvitz-Thompson estimator when the number of covariates is fixed. In this study, we investigate the performance of the generalized regression estimator when the number of covariates p is allowed to diverge as the sample size n increases. We examine two approaches where the model parameter is estimated using the weighted least squares method when p < n and the LASSO method when the model parameter is sparse. We show that under an assisted model and certain conditions on the joint distribution of the covariates as well as the divergence rates of n and p, the generalized regression estimator is asymptotically more efficient than the Horvitz-Thompson estimator, and is robust against model misspecification. We also study the consistency of variance estimation for the generalized regression estimator. Our theoretical results are corroborated by simulation studies and an example.

Investigating the Performance of Horvitz-Thompson and Generalized Regression Estimators in Small Domains with Application to Income and Expenditure of Households in Makurdi-Nigeria

In this study, efficiencies of Horvitz-Thompson (HT) and Generalized Regression (GREG) estimatorsare investigated in small domains namely Domain 1, 2 and 3. Efficiency criteria include the standarderror of the estimates (SE) and coefficient of variation (CV) Computed for the study population ofsize 1052 households consisting of domain size of 885, 151 and 16 and domain samples sizes of 167,29 and 3 respectively for Domains 1, 2 and 3. The estimates produced by HT estimator GREGestimator performs better than HT estimator with domain