scholarly journals Improved generalized family of estimators of population mean using information on transformed auxiliary variables

2018 ◽  
pp. 913-934 ◽  
Author(s):  
Housila P. Singh ◽  
Anita Yadav
Keyword(s):  
Mean Squared Error ◽  
Degree Of Approximation ◽  
Auxiliary Variables ◽  
Optimum Conditions ◽  
Study Variable ◽  
Population Mean ◽  
Mean Squared Errors ◽  
Squared Error

This paper addresses the problem of estimating the population mean  of the study variable using information on transformed auxiliary variables. In addition to many, Yasmeen et al (2015) estimator shown to the members of the suggested classes of estimators. We have derived the bias and mean squared error (MSE) of the suggested classes of estimators to the first degree of approximation. We have obtained the optimum conditions for which the suggested classes of estimators have minimum mean squared errors. It has been shown that the proposed classes of estimators are more efficient than the estimators recently envisaged by Yasmeen et al (2015) and other existing estimators.

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 of Population Mean Under Systematic Sampling

2021 ◽  
Vol 3 (1) ◽  
pp. 15-27
Author(s):  
Shagufta Mehnaz ◽  
Shakeel Ahmed
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Information ◽  
Degree Of Approximation ◽  
Systematic Sampling ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Population Mean ◽  
Sampling Schemes ◽  
Squared Error ◽  
Improved Estimators

Auxiliary information is very important in constructing estimators for the population parameters for increasing the efficiency different sampling schemes. In this paper, we consider the problem of estimation of population mean using information on auxiliary variables in systematic sampling. We derive the expressions for the bias and mean squared error (MSE) of the suggested estimators up to the 1st degree of approximation. Proposed estimators are compared with usual mean estimator in systematic sampling scheme theoretically as well as empirically.

scholarly journals Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation

2013 ◽  
Vol 31 (1) ◽  
pp. 39 ◽  
Author(s):  
M. Iqbal Jeelani ◽  
S. Maqbool
Keyword(s):  
Linear Combination ◽  
Auxiliary Variable ◽  
Degree Of Approximation ◽  
Linear Combinations ◽  
Study Variable ◽  
Population Mean ◽  
Mean Squared Errors ◽  
Ratio Estimators ◽  
Coefficient Of Skewness ◽  
Better Than

The present paper deals with the estimation of population mean of the study variable using the linear combination of known population values of coefficient of skewness and quartile deviation of auxiliary variable. Two modified ratio estimators for estimation of population mean of the study variable involving the above linear combinations are being used. Mean squared errors and biases up to the first degree of approximation are derived and compared with the proposed modified ratio estimators. The proposed modified ratio estimators perform better than the existing ratio estimators. The empirical study has been carried out in support of the results.

scholarly journals Adapted Factor-Type Imputation Strategies

2016 ◽  
Vol 8 (3) ◽  
pp. 321-339
Author(s):  
R. Pandey ◽  
K. Yadav ◽  
N. S. Thakur
Keyword(s):  
Relative Efficiency ◽  
Mean Squared Error ◽  
Data Sets ◽  
Optimum Conditions ◽  
Population Mean ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
The Mean ◽  
Factor Type ◽  
Percentage Relative Efficiency

The present paper provides alternative improved Factor-Type (F-T) estimators of population mean in presence of item non-response for the practitioners. The proposed estimators have been shown to be more efficient than the four existing estimators which are more efficient than the usual ratio and the mean estimators. Optimum conditions for minimum mean squared error are obtained for the new estimators. Empirical comparisons based on three different data sets establish that the proposed estimators record least mean squared error and hence a substantial gain in Percentage Relative Efficiency (P.R.E.), over these five contemporary estimators.

scholarly journals Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling

2017 ◽  
Vol 1 ◽  
pp. 1-14
Author(s):  
Subramani Jambulingam ◽  
Ajith S. Master
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Study Variable ◽  
Population Mean ◽  
Squared Error ◽  
Product Estimator ◽  
Almost Unbiased

Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

scholarly journals Calibration-Based Estimators using Different Distance Measures under Two Auxiliary Variables: A Comparative Study

2021 ◽  
Vol 19 (1) ◽  
pp. 2-20
Author(s):  
Piyush Kant Rai ◽  
Alka Singh ◽  
Muhammad Qasim
Keyword(s):  
Mean Squared Error ◽  
Real Life ◽  
Distance Functions ◽  
Distance Measures ◽  
Auxiliary Variables ◽  
Data Set ◽  
Life Data ◽  
Squared Error ◽  
Real Life Data ◽  
Relative Root

This article introduces calibration estimators under different distance measures based on two auxiliary variables in stratified sampling. The theory of the calibration estimator is presented. The calibrated weights based on different distance functions are also derived. A simulation study has been carried out to judge the performance of the proposed estimators based on the minimum relative root mean squared error criterion. A real-life data set is also used to confirm the supremacy of the proposed method.

scholarly journals Comparison of different lactation curve models in Holstein cows raised on a farm in the south-eastern Anatolia region

2008 ◽  
Vol 51 (4) ◽  
pp. 329-337
Author(s):  
Ö. Koçak ◽  
B. Ekiz
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Exponential Model ◽  
Eastern Anatolia ◽  
Mean Squared Errors ◽  
Squared Error ◽  
Lactation Curve ◽  
Daily Milk Yield ◽  
Daily Milk

Abstract. The objective of this study was to compare the goodness of fit of seven mathematical models (including the gamma function, the exponential model, the mixed log model, the inverse quadratic polynomial model and their various modifications) on daily milk yield records. The criteria used to compare models were mean R2, root mean squared errors (RMSE) and difference between actual and predicted lactation milk yields. The effect of lactation number on curve parameters was significant for models with three parameters. Third lactation cows had the highest intercept post-calving, greatest incline between calving and peak milk yield and greatest decline between peak milk yield and end of lactation. Latest peak production occurred in first lactation for all models, while third lactation cows had the earliest day of peak production. The R2 values ranged between 0.590 and 0.650 for first lactation, between 0.703 and 0.773 for second lactation and between 0.686 and 0.824 for third lactation, depending on the model fitted. The root mean squared error values of different models varied between 1.748 kg and 2.556 kg for first parity cows, between 2.133 kg and 3.284 kg for second parity cows and between 2.342 kg and 7.898 kg for third parity cows. Lactation milk yield deviations of Ali and Schaeffer, Wilmink and Guo and Swalve Models were close to zero for all lactations. Ali and Schaeffer Model had the highest R2 for all lactations and also yielded smallest RMSE and actual and predicted lactation milk yield differences. Wilmink and Guo and Swalve Models gave better fit than other three parameter models.

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

2022 ◽  
pp. 62-85
Author(s):  
Carlos N. Bouza-Herrera ◽  
Jose M. Sautto ◽  
Khalid Ul Islam Rather
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Auxiliary Variables ◽  
Mild Conditions ◽  
Squared Error ◽  
The Mean ◽  
Better Than

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

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 Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

2020 ◽  
Vol 8 (2) ◽  
pp. 49-56
Author(s):  
Akan Anieting
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Variable ◽  
Stratified Sampling ◽  
Second Phase ◽  
Two Phase ◽  
Population Mean ◽  
Squared Error ◽  
Large Sample Approximation ◽  
Sample Approximation ◽  
Phase Sample

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

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