On the Admissibility of the Symmetrized Des Raj Estimator for PPSWOR Samples of Size Two

1980 ◽  
Vol 29 (1-2) ◽  
pp. 35-44 ◽  
Author(s):  
S. Sengupta
Keyword(s):  
Population Size ◽  
Sampling Design ◽  
Finite Population ◽  
Ratio Estimator ◽  
Population Total ◽  
Sample Mean ◽  
Unbiased Estimators ◽  
Linear Estimators

The symmetrized Des Raj estimator for a finite population total based on a PPSWOR sample of size two is shown to be admissible within (i) the class of all linear estimators and (ii) the class of all unbiased estimators. In this connection we have obtained a class of admissible linear estimators of the population total which includes the sample mean multiplied by the population size and the classical ratio estimator for any arbitrary sampling design.

scholarly journals A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total

2019 ◽  
Vol 8 (3) ◽  
pp. 83
Author(s):  
Langat Reuben Cheruiyot ◽  
Odhiambo Romanus Otieno ◽  
George O. Orwa
Keyword(s):  
Boundary Problem ◽  
Nonparametric Regression ◽  
Finite Population ◽  
Simulated Data ◽  
The Other ◽  
Ratio Estimator ◽  
Regression Estimator ◽  
Population Total ◽  
Parametric Regression ◽  
Model Based

This study explores the estimation of finite population total. For many years design-based approach dominated the scene in statistical inference in sample surveys. The scenario has since changed with emergence of the other approaches (Model-Based, Model-Assisted and the Randomization-Assisted), which have proved to rival the conventional approach. This paper focuses on a model based approach. Within this framework a nonparametric regression estimator for finite population total is developed. The nonparametric technique has been found from previous studies to be advantageous than its parametric counterpart in terms of robustness and flexibility.  Kernel smoother has been used in construction of the estimator. The challenge of the boundary problem encountered with the Nadaraya-Watson estimator has been addressed by modifying it using reflection technique. The performance of the proposed estimator has been compared to the design-based Horvitz Thompson estimator and the model –based nonparametric regression estimator proposed by (Dorfman, 1992) and the ratio estimator using simulated data.

scholarly journals A Stopping Rule for Simulation‑Based Estimation of Inclusion Probabilities

2020 ◽  
Vol 4 (349) ◽  
pp. 67-80
Author(s):  
Wojciech Gamrot
Keyword(s):  
Computational Complexity ◽  
Sampling Design ◽  
Finite Population ◽  
Simulation Experiment ◽  
Population Parameters ◽  
Sampling Weights ◽  
Population Total ◽  
Inclusion Probabilities ◽  
Simulation Based ◽  
Important Challenge

Design‑based estimation of finite population parameters such as totals usually relies on the knowledge of inclusion probabilities characterising the sampling design. They are directly incorporated into sampling weights and estimators. However, for some useful sampling designs, these probabilities may remain unknown. In such a case, they may often be estimated in a simulation experiment which is carried out by repeatedly generating samples using the same sampling scheme and counting occurrences of individual units. By replacing unknown inclusion probabilities with such estimates, design‑based population total estimates may be computed. The calculation of required sample replication numbers remains an important challenge in such an approach. In this paper, a new procedure is proposed that might lead to the reduction in computational complexity of simulations.

Admissibility of the Symmetrized Des Raj Estimator for Fixed Size Sampling Designs of Size Two

1982 ◽  
Vol 31 (3-4) ◽  
pp. 201-206 ◽  
Author(s):  
S. Sengupta
Keyword(s):  
Sampling Design ◽  
Finite Population ◽  
Fixed Size ◽  
Population Total

An estimator identical in form with the symmetrized Des Raj estimator based on a PPSWOR sampling design of size two is shown to be admissible within the class of all estimators of a finite population total for any fixed size sampling design of size two.

scholarly journals Adaptive two-stage inverse sampling design to estimate density, abundance, and occupancy of rare and clustered populations

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255256
Author(s):  
Mohammad Salehi ◽  
David R. Smith
Keyword(s):  
Binary Data ◽  
Sampling Design ◽  
A Priori ◽  
Cluster Sampling ◽  
Adaptive Cluster Sampling ◽  
Inverse Sampling ◽  
Two Stage ◽  
Population Total ◽  
Unbiased Estimators ◽  
Final Sample

Sampling rare and clustered populations is challenging because of the effort required to find rare units. Heuristically, a practitioner would prefer to discontinue sampling in areas where rare units of interest are apparently extremely sparse or absent. We take advantage of the characteristics of inverse sampling to adaptively inform practitioners when it is efficient to move on to sample new areas. We introduce Adaptive Two-stage Inverse Sampling (ATIS), which is designed to leave a selected area after observation of an a priori number of only non-rare units and to continue sampling in the area when rare units are observed. ATIS is efficient in many cases and yields more rare units than conventional sampling for a rare and clustered population. We derive unbiased estimators of population total and variance. We also introduce an easy-to-compute estimator, which is nearly as efficient as the unbiased estimator. A simulation study on a rare plant population of buttercups (Ranunculus) shows that ATIS even with the easy-to-compute estimator is more efficient than its conventional sampling counterparts and is more efficient than Two-stage Adaptive Cluster Sampling (TACS) for small and moderate final sample sizes. Additional simulations reveal that ATIS is efficient for binary data (e.g., presence or absence) whereas TACS is inefficient for binary data. The overall results indicate that ATIS is consistently efficient compared to conventional sampling and to adaptive cluster sampling in some important cases.

scholarly journals Estimation of the current population total for a four-phase sampling design

2016 ◽  
Vol 21 (2) ◽  
pp. 241-260
Author(s):  
Viktoras Chadyšas ◽  
Danutė Krapavickaitė
Keyword(s):  
Sampling Design ◽  
Finite Population ◽  
Auxiliary Information ◽  
Real Data ◽  
Simple Random Sampling ◽  
Two Phase ◽  
Successive Sampling ◽  
Population Total ◽  
Sampling Without Replacement ◽  
Phase Sampling

The combined ratio-type estimators of the finite population total and their variances in the case of sample rotation for two-phase and four-phase sampling schemes are constructed in the paper. Combined estimators of the finite population total without and with the use of auxiliary information known from the previous survey are built. Two types of sampling design are used for sample selection in each of the phases: simple random sampling without replacement and successive sampling without replacement with probabilities proportional to size. A simulation study, based on the real data, is performed, and the accuracy of the estimators proposed is compared.

scholarly journals Modified Ratio-Cum-Product Estimators of Population Mean Using Two Auxiliary Variables

2020 ◽  
pp. 55-65
Author(s):  
J. O. Muili ◽  
E. N. Agwamba ◽  
Y. A. Erinola ◽  
M. A. Yunusa ◽  
A. Audu ◽  
...  
Keyword(s):  
Random Sampling ◽  
Finite Population ◽  
Simple Random Sampling ◽  
Degree Of Approximation ◽  
Ratio Estimator ◽  
Auxiliary Variables ◽  
Sampling Without Replacement ◽  
Sample Mean ◽  
Population Mean ◽  
Product Estimator

A percentile is one of the measures of location used by statisticians showing the value below which a given percentage of observations in a group of observations fall. A family of ratio-cum-product estimators for estimating the finite population mean of the study variable when the finite population mean of two auxiliary variables are known in simple random sampling without replacement (SRSWOR) have been proposed. The main purpose of this study is to develop new ratio-cum-product estimators in order to improve the precision of estimation of population mean in sample random sampling without replacement using information of percentiles with two auxiliary variables. The expressions of the bias and mean square error (MSE) of the proposed estimators were derived by Taylor series method up to first degree of approximation. The efficiency conditions under which the proposed ratio-cum-product estimators are better than sample man, ratio estimator, product estimator and other estimators considered in this study have been established. The numerical and empirical results show that the proposed estimators are more efficient than the sample mean, ratio estimator, product estimator and other existing estimators.

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