Usual Regression Estimator Research Articles

Noniterative adjustment to regression estimators with population-based auxiliary information for semiparametric models.

Disease registries, surveillance data, and other datasets with extremely large sample sizes become increasingly available in providing population-based information on disease incidence, survival probability, or other important public health characteristics. Such information can be leveraged in studies that collect detailed measurements but with smaller sample sizes. In contrast to recent proposals that formulate additional information as constraints in optimization problems, we develop a general framework to construct simple estimators that update the usual regression estimators with some functionals of data that incorporate the additional information. We consider general settings that incorporate nuisance parameters in the auxiliary information, non-i.i.d. data such as those from case-control studies, and semiparametric models with infinite-dimensional parameters common in survival analysis. Details of several important data and sampling settings are provided with numericalexamples.

Comparison of Various Methods for Estimating Finite Population Total in Survey Sampling When Study Variable and Auxiliary Variable are Inversely Related

In the present paper, a model based calibration estimator of population total has been developed when study variable y and auxiliary variable x are inversely related. The relative performance of the proposed model based calibration estimator in comparison to model based estimator, the usual regression estimator and calibration based regression estimator have been examined by conducting a limited simulation study. In view of the results of the simulation study, it has been found that model based calibration estimator has outperformed the other estimators. However, calibration based regression estimator was found to be close to the model based calibration estimator.

Some classes of estimators in the presence of non-response using auxiliary attribute.

In this paper, possible solutions of problem of non-response in the variable of interest are proposed when information about an auxiliary attribute is available. By taking motivation from the previous work, modified classes have been suggested for estimating population mean. Two new generalized classes of estimators are presented along with their asymptotic biases and variances. Efficacy analysis of the suggested classes is acquired with the usual regression estimator. Two real examples have been provided to show the efficiency of the proposed design approach and comparison of suggested estimators with the linear regression estimator.

Alternative Ratio - Regression Type Estimator in Simple Random Sampling

In this study, an alternative ratio-regression type estimator was proposed which was compared with Kadilar and Cingi (2004), and Ekaete et al. (2014) estimators. This proposed estimator combined classical ratio estimator with our usual regression estimator. The same data set used by Kadilar and Cingi (2004) and Ekaete et al. (2014) were also used to determine the efficiency of this alternative ratio-regression type estimator. The finding was that, when α=1, Ekaete et al. (2014) was found to be better but  at , this alternative ratio-regression type estimator was said to be more efficient than both Kadilar and Cingi (2004), and Ekaete et al. (2014) estimators based on their estimated mean square error (mse).

Preliminary Test Regression Estimator When two Prior Values of Population Mean (μx) of an Auxiliary Variable (x) are Available

A regression estimator using two prior values of population mean (μx) of an auxiliary variable (x) is proposed after a preliminary test of closeness of these prior values to the true valueμx. The proposed preliminary test regression estimator has been found to be more efficient in general than the usual regression estimator when prior values are used in place of μxwithout preliminary test of significance. The efficiency of the proposed estimator over the usual regression estimator has also been computed for different values of Δ0, Δ1, n, and ρ, which showed considerable gain in precision.

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Stratified Random Sampling

This article addresses the problem of estimating the population mean in stratified random sampling using the information of an auxiliary variable. A class of estimators for population mean is defined with its properties under large sample approximation. In particular, various classes of estimators are identified as particular member of the suggested class. It has been shown that the proposed class of estimators is better than usual unbiased estimator, usual combined ratio estimator, usual product estimator, usual regression estimator and Koyuncu and Kadilar (2009) class of estimators. The results have been illustrated through an empirical study.

Calibration Approach-Based Regression-Type Estimator for Inverse Relationship Between Study and Auxiliary Variable

A regression-type estimator of population total is developed using the calibration approach under the assumption that the auxiliary variable is negatively correlated with the study variable. An estimator of the variance of the proposed estimator is developed. In addition, a higher order calibration approach has been described for the estimator of the variance of the proposed estimator. When the auxiliary information is not available on all the population units, then a two-phase sampling approach has been suggested. Theoretical results obtained are demonstrated through simulation studies and also with real data. Empirical results show that the proposed estimator outperforms the usual regression estimator in terms of the criteria of bias and mean square error.

An improved estimator using two auxiliary attributes

In the present study, we propose two new estimators for population mean using Kadilar and Cingi (2005) [2] and Lu et al. (2010) [9] estimators in the case when the information is available in form of attributes. Expressions for the MSE’s of the proposed estimator are derived up to the first degree of approximation. The theoretical conditions have also been verified by a numerical example. It has been shown that the proposed estimators are more efficient than usual regression estimators.

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information

This article addresses the problem of estimating the population mean in the presence of auxiliary information. A class of estimators for population mean is defined. Asymptotic expressions of the bias and mean squared error of the proposed class of estimators were obtained. Asymptotic optimum estimator (AOE) in the proposed class of estimators was identified along with its mean squared error formula. It has been shown that the proposed class of estimators is more efficient than the usual regression estimator and Khoshnevisan et al. (2007), Singh et al. (2007), and Koyuncu and Kadilar (2009a) classes of estimators.

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Systematic Sampling

This article addresses the problem of estimating the population mean in systematic sampling using information on an auxiliary variable. A class of estimators for the population mean is defined with its properties under large sample approximation. It has been shown that the proposed class of estimators is better than the usual unbiased estimator, Swain (1964) estimator, Shukla (1971) estimator, and usual regression estimator. The results have been illustrated through an empirical study.

Design-based regression estimators for spatial means of soil properties: the use of two-phase sampling when the means of the auxiliary variables are unknown

The accuracy of design-based sampling strategies can be increased by using regression models at the estimation stage. The usual regression estimator requires that the means of the auxiliary variables are known. If these means are unknown, then it sometimes pays to estimate these from a large preliminary sample that is subsampled in the second phase. Two types of regression estimator, the simple regression estimator and the ratio estimator are compared with the π* estimator in two case studies. In one study, a simulated, bivariate field (correlation coefficient 0.841) was repeatedly sampled by Simple Random Sampling in both phases. The standard error of the simple regression estimator was 61% to 81% of the standard error of the π* estimator; for the ratio estimator, this percentage varied from 78% to 90%. Given the size of the subsample, the gain in precision depends on the size of the first phase sample and the quality of the model. For a sample size ratio of four, the gain was 70% to 75% of the gain that would be achieved if the mean of the auxiliary variable were known. The gain in precision achieved by the ratio estimator, assuming incorrectly that the intercept is 0, was 50% to 60% of the gain achieved by the regression estimator. Despite the incorrect model assumptions, the ratio estimator was approximately design-unbiased, and the confidence intervals were valid. For small sample sizes in the second phase, the ratio estimator performs even slightly better than the regression estimator with respect to validity. This stresses the importance of using simple models. In a second study, the estimated spatial means of the Mean Highest Water table and Mean Lowest Water table of six map units were estimated by Stratified Simple Random Sampling in both phases in combination with the regression estimator that uses the starting depth of hydromorphic properties in the soil profile as an auxiliary variable. The gain in precision did not outweigh the extra costs of collecting the auxiliary data.

On constructing almost unbiased estimators of finite population mean using transformed auxiliary variable

This paper is intended as an investigation of constructing almost unbiased estimators of finite population mean by suitably combining a set of transformed estimators. A generalization of Tracy, Singh and Singh (1999) estimator is suggested, and, to the first degree of approximation, each member of the proposed class is as efficient as the usual regression estimator. Further, it is proved that Reddy (1973) estimator is also a particular case of the proposed class. To the second degree of approximation, a new almost unbiased estimator is established. Moreover, an empirical study is carried out in order to understand better the performance of the new estimator compared to the usual unbiased B, ratio BR and Tracy et al. (1999) estimators.

Preliminary test estimators in double sampling with two auxiliary variables

An attempt has been mads to suggest some estimators for population mean in double sampling with two auxiliary variables., alternative to the usual regression estimator. When the experimenter has partial Information about the mean of the auxiliary variable or variables, preliminary test estimators can be used. The bias, mean square error, relative efficiency and optimum allocation of sample sizes are obtained for the suggested estimators.

Non-existence of an optimum estimator in a class of ratio estimators

A number of estimators formulated in the field of the ratio method of estimation has been presented. A class of estimators encompassing these estimators is constructed. It is noted that an optimum estimator does not exist uniformly in this class. The “Optimum” so obtained reduces to the usual regression estimator.

Sampling schemes providing unbaised regression estimators

SUMMARY A sampling scheme is proposed for which the usual regression estimator is unbiased. Another sampling scheme with an unbiased regression-type estimator is also considered. On comparing the efficiencies of these sampling strategies with some existing strategies, the performance of the first of the new schemes is found to be highly satisfactory.

The Precision of Some Unbiased Regression Estimators

In the development of the statistical theory of sample surveys, one of the main aims has been to improve the estimates that are obtained from the data. One method which has been used quite extensively to create estimators with more advantageous variances is the utilization of auxiliary information. Analytically this usually takes the form of a random sample of n pairs (yi , xi) from a population of size N. The problem is to estimate the population y mean (guy) relative to the assumption that the population x mean (Ax) is known exactly. This information can be utilized in the form of ratio and regression estimators. The distinction between ratio and regression estimators is that a regression estimator is invariant under linear x transformations and undergoes the same linear transformation as y. Ratio estimators have the same property but only for scale changes. Both types of estimator result in a comparison of the over-all variation in the y characteristic to the residual variation about the relationship of y and x. Ratio estimators are inefficient if the relationship between y and x does not pass through the origin; regression estimators do not require this. Descriptions can be found, for example, in Cochran [1953]. The usual regression estimator assumes a linear model,

The Estimation of Repeatability and Heritability from Records Subject to Culling

In any animal breeding selection programme, estimates of repeatability and heritability are needed to choose between the various selection schemes available and also to ensure that the highest possible genetic gains are obtained from the chosen scheme. Estimates of repeatability and heritability are generally subject to large sampling errors. Therefore, the most efficient methods of estimation should be used even if they do involve rather lengthy computations. In this paper, the maximum likelihood estimation of repeatability and heritability from records subject to culling will be considered. The more usual regression estimators are often very inefficient compared with these maximum likelihood estimators. Suppose that we wish to estimate the repeatability of lactation yield in a herd of dairy cattle. We shall assume that only first and second lactation yields are available and that, if there had been no culling (i.e., if all the cows had had second records as well as first records), the first and second records would have been normally distributed over the herd with means i,u and u2 , variances oC and o? and covariance between the two records of the same cow 12 . The first and second records of cow i will be written yi, and Yi2 respectively. The assumption of normality for the distributions will probably be a reasonably good approximation unless the herd can be split into groups so that any two cows in the same group are much more alike than two cows in different groups. These groups may, for example, be groups of daughters of the same sire or groups of cows according to the year in which they gave their first record or the month in which they calved. Methods are available for making allowances for such groupings, but they will be assumed absent in the rest of this paper. Very rarely will the culling