Computation of Improved Searls Estimation of Population Variance Using Robust Auxiliary Parameters

2020 ◽  
Vol 13 ◽  
Author(s):  
S. K. Yadav ◽  
Dinesh Sharma ◽  
Julius Alade
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Efficient Estimation ◽  
Data Sets ◽  
Population Variance ◽  
Practical Applications ◽  
Squared Error ◽  
Natural Data ◽  
R Programming

Introduction: Variation is an inherent phenomenon whether in nature made things or man made. Thus, it looks important to estimate this variation. Various authors have worked in the direction of improved estimation of population variance utilizing the known auxiliary parameters for better policy making. Methods: In this article, a new searls ratio type class of estimator is suggested for elevated estimation of population variance of main variable. As the suggested estimator is biased, so its bias and mean squared error (MSE) have been derived up to the approximation of order-one. The optimum values for the Searls characterizing scalars are obtained. The minimum MSE of the introduced estimator is obtained for the optimum Searls characterizing scalars. A theoretical comparison between suggested estimator and the competing estimators has been made through their mean squared errors. The efficiency conditions of suggested estimator over competing estimators are also obtained. These theoretical conditions are verified using some natural data sets. The computation of R codes for the biases and MSEs of the suggested and competing estimators are developed and are used for three natural populations in Naz et al. (2019). The estimator with least MSE is recommended for practical utility. The empirical study has been done using R programming. Results: The MSEs of different competing and the suggested estimators are obtained for three natural populations. The estimator under comparison with the least MSE is recommended for practical applications. Discussion: The aim to search for the most efficient estimation for improved estimation, is fulfilled through the proper use of the auxiliary parameters obtained from the known auxiliary variable. The suggested estimator may be used for elevated estimation of population variance. Conclusion: The introduced estimator is having least MSE as compared to competing estimators of popularion variance for all three natural populations. Thus it may be recommended for the application in various fields.

scholarly journals A Class of Modified Ratio Estimators for Estimation of Population Variance

2015 ◽  
Vol 11 (1) ◽  
pp. 91-114 ◽  
Author(s):  
J. Subramani ◽  
G. Kumarapandiyan
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Variance Estimators ◽  
Squared Error ◽  
Ratio Estimators ◽  
Better Than

Abstract In this paper we have proposed a class of modified ratio type variance estimators for estimation of population variance of the study variable using the known parameters of the auxiliary variable. The bias and mean squared error of the proposed estimators are obtained and also derived the conditions for which the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators. Further we have compared the proposed estimators with that of the traditional ratio type variance estimator and existing modified ratio type variance estimators for certain natural populations.

scholarly journals An Improved Ratio-Type Variance Estimator by Using Linear Combination of Diferent Measures of Location

2018 ◽  
Vol 3 (1) ◽  
pp. 24-32
Author(s):  
Muhammad Ali ◽  
Muhammad Khalil ◽  
Muhammad Hanif ◽  
Nasir Jamal ◽  
Usman Shahzad
Keyword(s):  
Research Study ◽  
Mean Squared Error ◽  
Auxiliary Variable ◽  
The Other ◽  
Primary Data ◽  
Data Sets ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Squared Error

In this research study, modified family of estimators is proposed to estimate the population variance of the study variable when the population variance, quartiles, median and the coefficient of correlation of auxiliary variable are known. The expression of bias and mean squared error (MSE) of the proposed estimator are derived. Comparisons of the proposed estimator with the other existing are conducted estimators. The results obtained were illustrated numerically by using primary data sets. Theoretical and numerical justification of the proposed estimator was done to show its dominance.

scholarly journals Variance Estimator Using Tri-mean and Inter Quartile Range of Auxiliary Variable

2017 ◽  
Vol 1 ◽  
pp. 83-91
Author(s):  
S.K. Yadav ◽  
Sheela Misra ◽  
S.S. Mishra ◽  
Shankar Prasad Khanal
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Population Parameter ◽  
Variance Estimator ◽  
Population Variance ◽  
Inter Quartile Range ◽  
First Order ◽  
Squared Error ◽  
Quartile Range

Background: Whenever the population is large and it is very time taking and costly to take observation on each unit of the population then sampling is the only way to get the appropriate estimate of the population parameter under consideration. Many authors have given many estimators for estimating population variance with greater efficiency.Objective: The objective of the study is to search for more efficient estimator than the competing estimators of population variance of study variable.Materials and Methods: The estimator utilizing information on tri-mean and inter quartile range of auxiliary variable has been is developed. The expressions for the bias and mean squared error (MSE) of the proposed estimator have been derived up to the first order of approximation. A theoretical comparison of the proposed estimator has been made with the competing estimators of population variance.Results: The theoretical findings have been justified with the help of numerical example from some natural populations. It has been found that the proposed estimator is best among the competing estimators of population variance as it has least mean squared error among them.Conclusion: Since the proposed estimator is best among the competing estimator of the population variance, therefore it must be used for the improved estimation of population variance.Nepalese Journal of Statistics, 2017, Vol. 1, 83-91

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.

scholarly journals A Family of Difference-Cum-Exponential Type Estimators for Estimating the Population Variance Using Auxiliary Information in Sample Surveys

2014 ◽  
Vol 1 ◽  
pp. 15-21
Author(s):  
H.S. Jhajj ◽  
Kusam Lata
Keyword(s):  
Linear Regression ◽  
Exponential Type ◽  
Random Sampling ◽  
Sampling Design ◽  
Mean Squared Error ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Double Sampling ◽  
Population Variance ◽  
Squared Error

Using auxiliary information, a family of difference-cum-exponential type estimators for estimating the population variance of variable under study have been proposed under double sampling design. Expressions for bias, mean squared error and its minimum values have been obtained. The comparisons have been made with the regression-type estimator by using simple random sampling at both occasions in double sampling design. It has also been shown that better estimators can be obtained from the proposed family of estimators which are more efficient than the linear regression type estimator. Results have also been illustrated numerically as well asgraphically.

scholarly journals New Approaches for Quantitative Reconstruction of Radiation Dose in Human Blood Cells

2019 ◽  
Author(s):  
Shanaz A. Ghandhi ◽  
Igor Shuryak ◽  
Shad R. Morton ◽  
Sally A. Amundson ◽  
David J. Brenner
Keyword(s):  
Radiation Dose ◽  
Mean Squared Error ◽  
Data Sets ◽  
Reconstruction Method ◽  
Dose Reconstruction ◽  
New Methods ◽  
Rapid Assays ◽  
Squared Error ◽  
Gene Sets ◽  
Human Blood Cells

AbstractIn the event of a nuclear attack or radiation event, there would be an urgent need for assessing and reconstructing the dose to which hundreds or thousands of individuals were exposed. These measurements would need a rapid assay to facilitate triage and medical management for individuals based on dose. Our approaches to development of rapid assays for reconstructing dose, using transcriptomics, have led to identification of gene sets that have potential to be used in the field; but need further testing. This was a proof-of-principle study for new methods using radiation-responsive genes to generate quantitative, rather than categorical, radiation-dose reconstructions based on a blood sample. We used a new normalization method to reduce effects of variability of gene signals in unirradiated samples across studies; developed a quantitative dose-reconstruction method that is generally under-utilized compared to categorical methods; and combined these to determine a gene-set as a reconstructor. Our dose-reconstruction biomarker was trained on two data sets and tested on two independent ones. It was able to predict dose up to 4.5 Gy with root mean squared error (RMSE) of ± 0.35 Gy on test datasets (same platform), and up to 6.0 Gy with RMSE of 1.74 Gy on another (different platform).

scholarly journals Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving

Risks ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 112
Author(s):  
Nataliya Chukhrova ◽  
Arne Johannssen
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Mean Squared Error ◽  
Learning Algorithms ◽  
State Space Models ◽  
Future Research ◽  
Practical Applications ◽  
Squared Error

In stochastic claims reserving, state space models have been used for almost 40 years to forecast loss reserves and to compute their mean squared error of prediction. Although state space models and the associated Kalman filter learning algorithms are very powerful and flexible tools, comparatively few articles on this topic were published during this period. Most recently, several articles have been published which highlight the benefits of state space models in stochastic claims reserving and may lead to a significant increase in its popularity for applications in actuarial practice. To further emphasize the merits of these papers, this commentary highlights various additional aspects that are useful for practical applications and offer some fruitful directions for future research.

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 Additive Dose Response Models: Explicit Formulations and the Loewe Additivity Consistency Condition

2017 ◽  
Author(s):  
Simone Lederer ◽  
Tjeerd M. H. Dijkstra ◽  
Tom Heskes
Keyword(s):  
Mean Squared Error ◽  
Reference Model ◽  
Consistency Condition ◽  
Data Sets ◽  
The Novel ◽  
Response Models ◽  
Reference Models ◽  
Squared Error ◽  
Common Principle ◽  
Loewe Additivity

AbstractHigh-throughput techniques allow for massive screening of drug combinations. To find combinations that exhibit an interaction effect, one filters for promising compound combinations by comparing to a response without interaction. A common principle for no interaction is Loewe Additivity which is based on the assumption that no compound interacts with itself and that doses of both compounds for a given effect are equivalent. For the model to be consistent, the doses of both compounds have to be proportional. We call this restriction the Loewe Additivity Consistency Condition (LACC). We derive explicit and implicit null reference models from the Loewe Additivity principle that are equivalent when the LACC holds. Of these two formulations, the implicit formulation is the known General Isobole Equation [1], whereas the explicit one is the novel contribution. The LACC is violated in a significant number of cases. In this scenario the models make different predictions. We analyze two data sets of drug screening that are non-interactive [2, 3] and show that the LACC is mostly violated and Loewe Additivity not defined. Further, we compare the measurements of the non-interactive cases of both data sets to the theoretical null reference models in terms of bias and mean squared error. We demonstrate that the explicit formulation of the null reference model leads to smaller mean squared errors than the implicit one and is much faster to compute.

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