Large Sample Approximation of the Distribution for Convex-Hull Estimators of Boundaries

2006 ◽  
Vol 33 (1) ◽  
pp. 139-151 ◽  
Author(s):  
S.-O. JEONG ◽  
B. U. PARK
Keyword(s):  
Convex Hull ◽  
Large Sample ◽  
Large Sample Approximation ◽  
Sample Approximation

scholarly journals A New Exponential Approach for Reducing the Mean Squared Errors of the Estimators of Population Mean Using Conventional and Non-Conventional Location Parameters

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Housila P. Singh ◽  
Anita Yadav
Keyword(s):  
Large Sample ◽  
Population Mean ◽  
Mean Squared Errors ◽  
Large Sample Approximation ◽  
Location Parameters ◽  
Sample Approximation ◽  
The Mean

Classes of ratio-type estimators t (say) and ratio-type exponential estimators te (say) of the population mean are proposed, and their biases and mean squared errors under large sample approximation are presented. It is the class of ratio-type exponential estimators te provides estimators more efficient than the ratio-type estimators.

scholarly journals A family of estimators of population mean using multi-auxiliary variate and post-stratification

2010 ◽  
Vol 15 (2) ◽  
pp. 233-253 ◽  
Author(s):  
Gajendra K. Vishwakarma ◽  
Housila P. Singh ◽  
Sarjinder Singh
Keyword(s):  
Empirical Study ◽  
Stratified Sampling ◽  
Large Sample ◽  
Population Mean ◽  
Auxiliary Variate ◽  
Large Sample Approximation ◽  
Sample Approximation ◽  
Optimum Estimator ◽  
Class Of Estimators ◽  
Approximate Variance

This paper suggests a family of estimators of population mean using multiauxiliary variate based on post-stratified sampling and its properties are studied under large sample approximation. Asymptotically optimum estimator in the class is identified alongwith its approximate variance formulae. The proposed class of estimators is also compared with corresponding unstratified class of estimators based on estimated optimum value. At the end, an empirical study has been carried out to support the proposed methodology.

scholarly journals On Using the Conventional and Nonconventional Measures of the Auxiliary Variable for Mean Estimation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Javid Shabbir ◽  
Sat Gupta ◽  
Ronald Onyango
Keyword(s):  
Survey Research ◽  
Finite Population ◽  
Auxiliary Variable ◽  
Large Sample ◽  
New Class ◽  
Numerical Studies ◽  
Mean Estimation ◽  
Large Sample Approximation ◽  
Sample Approximation ◽  
Class Of Estimators

In this paper, we propose an improved new class of exponential-ratio-type estimators for estimating the finite population mean using the conventional and the nonconventional measures of the auxiliary variable. Expressions for the bias and MSE are obtained under large sample approximation. Both simulation and numerical studies are conducted to validate the theoretical findings. Use of the conventional and the nonconventional measures of the auxiliary variable is very common in survey research, but we observe that this does not add much value in many of the estimators except for our proposed class of estimators.

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 Prediction intervals for random-effects meta-analysis: A confidence distribution approach

2018 ◽  
Vol 28 (6) ◽  
pp. 1689-1702 ◽  
Author(s):  
Kengo Nagashima ◽  
Hisashi Noma ◽  
Toshi A Furukawa
Keyword(s):  
Random Effects ◽  
Prediction Interval ◽  
Meta Analysis ◽  
Prediction Intervals ◽  
Point Estimate ◽  
Random Effects Models ◽  
Confidence Distribution ◽  
Large Sample Approximation ◽  
Sample Approximation ◽  
Meta Analyses

Prediction intervals are commonly used in meta-analysis with random-effects models. One widely used method, the Higgins–Thompson–Spiegelhalter prediction interval, replaces the heterogeneity parameter with its point estimate, but its validity strongly depends on a large sample approximation. This is a weakness in meta-analyses with few studies. We propose an alternative based on bootstrap and show by simulations that its coverage is close to the nominal level, unlike the Higgins–Thompson–Spiegelhalter method and its extensions. The proposed method was applied in three meta-analyses.

scholarly journals On Improving Ratio/Product Estimator by Ratio/Product-cum-Mean-per-Unit Estimator Targeting More Efficient Use of Auxiliary Information

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Angela Shirley ◽  
Ashok Sahai ◽  
Isaac Dialsingh
Keyword(s):  
Auxiliary Information ◽  
Simple Random Sample ◽  
Sample Mean ◽  
Parameter Ratio ◽  
Large Sample Approximation ◽  
Product Estimator ◽  
Sample Approximation ◽  
The Mean ◽  
Classical Linear Regression ◽  
Linear Regression Estimator

To achieve a more efficient use of auxiliary information we propose single-parameter ratio/product-cum-mean-per-unit estimators for a finite population mean in a simple random sample without replacement when the magnitude of the correlation coefficient is not very high (less than or equal to 0.7). The first order large sample approximation to the bias and the mean square error of our proposed estimators are obtained. We use simulation to compare our estimators with the well-known sample mean, ratio, and product estimators, as well as the classical linear regression estimator for efficient use of auxiliary information. The results are conforming to our motivating aim behind our proposition.

scholarly journals Improved Exponential Dual to Ratio Type Imputation for Missing Data under Two-Phase Sampling

2021 ◽  
Vol 9 (8) ◽  
pp. 2338-2348
Author(s):  
B. K. Singh
Keyword(s):  
Missing Data ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Two Phase ◽  
Large Sample Approximation ◽  
Phase Sampling ◽  
Point Estimator ◽  
Sample Approximation ◽  
Two Populations ◽  
Two Phase Sampling

Abstract: In this paper, authors have proposed a class of exponential dual to ratio type compromised imputation technique and corresponding point estimator in two-phase sampling design. Two different sampling designs in two-phase sampling are compared under imputed data. The bias and M.S.E. of suggested estimator is derived in the form of population parameters using the concept of large sample approximation. Numerical study is performed over two populations using the expressions of bias and M.S.E. and efficiency compared with existing estimators. Keywords: Missing data, Bias, Mean squared error (M.S.E), Two-phase sampling, SRSWOR, Compromised Imputation (C.I.).

scholarly journals Efficient Estimator for Population Mean in Stratified Double Sampling in the Presence of Nonresponse Using One Auxiliary Variable

2021 ◽  
Vol 4 (2) ◽  
pp. 41-51
Author(s):  
A.E. Anieting ◽  
E. I. Enang ◽  
C. E. Onwukwe
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Variable ◽  
Double Sampling ◽  
Population Mean ◽  
Squared Error ◽  
Large Sample Approximation ◽  
Sample Approximation ◽  
Second Phases ◽  
Optimal Values

A modified form of the population mean estimator suggested by Anieting and Enang (2020) in stratified double sampling in the presence of nonresponse using a single auxiliary variable has been proposed. The Mean Squared Error (MSE) and the bias of the proposed estimator have been given using large sample approximation. The empirical study shows that the MSE of the suggested estimator is more efficient than all other existing estimators in the same scheme. Determination of the optimal values of the first and second phases samples has also been done

scholarly journals Sample size considerations for split-mouth design

2015 ◽  
Vol 26 (6) ◽  
pp. 2543-2551 ◽  
Author(s):  
Hong Zhu ◽  
Song Zhang ◽  
Chul Ahn
Keyword(s):  
Sample Size ◽  
Treatment Effect ◽  
Estimating Equation ◽  
Binary Outcomes ◽  
Distinct Advantage ◽  
Finite Sample ◽  
Large Sample Approximation ◽  
Parallel Group Design ◽  
Parallel Group ◽  
Sample Approximation

Split-mouth designs are frequently used in dental clinical research, where a mouth is divided into two or more experimental segments that are randomly assigned to different treatments. It has the distinct advantage of removing a lot of inter-subject variability from the estimated treatment effect. Methods of statistical analyses for split-mouth design have been well developed. However, little work is available on sample size consideration at the design phase of a split-mouth trial, although many researchers pointed out that the split-mouth design can only be more efficient than a parallel-group design when within-subject correlation coefficient is substantial. In this paper, we propose to use the generalized estimating equation (GEE) approach to assess treatment effect in split-mouth trials, accounting for correlations among observations. Closed-form sample size formulas are introduced for the split-mouth design with continuous and binary outcomes, assuming exchangeable and “nested exchangeable” correlation structures for outcomes from the same subject. The statistical inference is based on the large sample approximation under the GEE approach. Simulation studies are conducted to investigate the finite-sample performance of the GEE sample size formulas. A dental clinical trial example is presented for illustration.

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