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- Articles and reports: 12-001-X19960022973Description:
There exist well known methods due to Deville and Sárndal (1992) which adjust sampling weights to meet benchmark constraints and range restrictions. The resulting estimators are known as calibration estimators. There also exists an earlier, but perhaps not as well known, method due to Huang and Fuller (1978). In addition, alternative methods were developed by Singh (1993), who showed that similar to the result of Deville-Sárndal, all these methods are asymptotically equivalent to the regression method. The purpose of this paper is threefold: (i) to attempt to provide a simple heuristic justification of all calibration estimators (including both well known and not so well known) by taking a non-traditional approach; to do this, a model (instead of the distance function) for the weight adjustment factor is first chosen and then a suitable method of model fitting is shown to correspond to the distance minimization solution, (ii) to provide to practitioner computational algorithms as a quick reference, and (iii) to illustrate how various methods might compare in terms of distribution of weight adjustment factors, point estimates, estimated precision, and computational burden by giving numerical examples based on a real data set. Some interesting observations can be made by means of a descriptive analysis of numerical results which indicate that while all the calibration methods seem to behave similarly to the regression method for loose bounds, they however seem to behave differently for tight bounds.
Release date: 1997-01-30 - 2. Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization ArchivedArticles and reports: 12-001-X19960022978Description:
The use of auxiliary information in estimation procedures in complex surveys, such as Statistics Canada's Labour Force Survey, is becoming increasingly sophisticated. In the past, regression and raking ratio estimation were the commonly used procedures for incorporating auxiliary data into the estimation process. However, the weights associated with these estimators could be negative or highly positive. Recent theoretical developments by Deville and Sárndal (1992) in the construction of "restricted" weights, which can be forced to be positive and upwardly bounded, has led us to study the properties of the resulting estimators. In this paper, we investigate the properties of a number of such weight generating procedures, as well as their corresponding estimated variances. In particular, two variance estimation procedures are investigated via a Monte Carlo simulation study based on Labour Force Survey data; they are Jackknifing and Taylor Linearization. The conclusion is that the bias of both the point estimators and the variance estimators is minimal, even under severe "restricting" of the final weights.
Release date: 1997-01-30
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- Articles and reports: 12-001-X19960022973Description:
There exist well known methods due to Deville and Sárndal (1992) which adjust sampling weights to meet benchmark constraints and range restrictions. The resulting estimators are known as calibration estimators. There also exists an earlier, but perhaps not as well known, method due to Huang and Fuller (1978). In addition, alternative methods were developed by Singh (1993), who showed that similar to the result of Deville-Sárndal, all these methods are asymptotically equivalent to the regression method. The purpose of this paper is threefold: (i) to attempt to provide a simple heuristic justification of all calibration estimators (including both well known and not so well known) by taking a non-traditional approach; to do this, a model (instead of the distance function) for the weight adjustment factor is first chosen and then a suitable method of model fitting is shown to correspond to the distance minimization solution, (ii) to provide to practitioner computational algorithms as a quick reference, and (iii) to illustrate how various methods might compare in terms of distribution of weight adjustment factors, point estimates, estimated precision, and computational burden by giving numerical examples based on a real data set. Some interesting observations can be made by means of a descriptive analysis of numerical results which indicate that while all the calibration methods seem to behave similarly to the regression method for loose bounds, they however seem to behave differently for tight bounds.
Release date: 1997-01-30 - 2. Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization ArchivedArticles and reports: 12-001-X19960022978Description:
The use of auxiliary information in estimation procedures in complex surveys, such as Statistics Canada's Labour Force Survey, is becoming increasingly sophisticated. In the past, regression and raking ratio estimation were the commonly used procedures for incorporating auxiliary data into the estimation process. However, the weights associated with these estimators could be negative or highly positive. Recent theoretical developments by Deville and Sárndal (1992) in the construction of "restricted" weights, which can be forced to be positive and upwardly bounded, has led us to study the properties of the resulting estimators. In this paper, we investigate the properties of a number of such weight generating procedures, as well as their corresponding estimated variances. In particular, two variance estimation procedures are investigated via a Monte Carlo simulation study based on Labour Force Survey data; they are Jackknifing and Taylor Linearization. The conclusion is that the bias of both the point estimators and the variance estimators is minimal, even under severe "restricting" of the final weights.
Release date: 1997-01-30
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