scholarly journals Bootstrap, jackknife and Edgeworth approximations for finite population L-statistics

2010 ◽  
Vol 51 ◽  
Author(s):  
Andrius Čiginas
Keyword(s):  
Distribution Function ◽  
Edgeworth Expansion ◽  
Finite Population ◽  
Normal Approximation ◽  
Bootstrap Approximation ◽  
True Distribution

In this paper we give exact bootstrap estimators for the parameters defining one-term Edgeworth expansion of distribution function of finite population L-statistic and compare these estimators with corresponding jackknife estimators. We also compare `````` true’ distribution of L-statistic with its normal approximation, Edgeworth expansion, empirical Edgeworth expansion and bootstrap approximation.

Testing for individual sphericity in heterogeneous panels

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 740-747
Author(s):  
Simon A Broda
Keyword(s):  
Distribution Function ◽  
Normal Approximation ◽  
Empirical Work ◽  
Null Distribution ◽  
Saddlepoint Approximation ◽  
Test Statistic ◽  
Cross Sectional ◽  
P Values ◽  
Cross Sectional Dimension ◽  
Heterogeneous Panels

Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.

scholarly journals Approximations to distribution of median in stratified samples

2011 ◽  
Vol 52 ◽  
Author(s):  
Andrius Čiginas ◽  
Tomas Rudys
Keyword(s):  
Distribution Function ◽  
Explicit Expression ◽  
Normal Approximation ◽  
Sample Median ◽  
Numerical Examples ◽  
Type Approximation

We consider an Edgeworth type approximation to the distribution function of sample median in the case of stratified samples drawn without replacement. We give explicit expression of this approximation, and also its empirical version based on bootstrap. We compare their accuracy with that of the normal approximation by numerical examples.

scholarly journals Estimation of finite population distribution function with dual use of auxiliary information under non-response

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243584
Author(s):  
Sardar Hussain ◽  
Sohaib Ahmad ◽  
Sohail Akhtar ◽  
Amara Javed ◽  
Uzma Yasmeen
Keyword(s):  
Distribution Function ◽  
Finite Population ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Sample Distribution

In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.

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