Minimum Risk Point Estimation of Gini Index

De, Shyamal K.; Chattopadhyay, Bhargab

doi:10.1007/s13571-017-0140-3

Cited by 9 publications

(21 citation statements)

References 24 publications

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“…Proof. This proof is along the same lines as the proof of Lemma 7.7 of De and Chattopadhyay (2015). We note, (…”

mentioning

confidence: 70%

“…1 For details about reverse submartinagles and their properties, we refer to classic textbooks on probability theory and stochastic processes such as Loève (1963), Doob (1953) and others. Using several results of Sen and Ghosh (1981), Sen (1981), Lee (1990), Ghosh et al (1997), Gut (2009) and De and Chattopadhyay (2015) and also using properties of U-statistics we prove the following lemmas to prove the main theorem.…”

Section: Theoretical Resultsmentioning

confidence: 96%

“…. Using Lemma 7.7 of De and Chattopadhyay (2015), Lemma 9.2.4 of Ghosh et al (1997) and the conditions of Lemma Equation 7, we conclude that E 11 = O ( √ /n c ). Similarly, using the Cauchy-Schwarz inequality, Lemma 6 and the conditions of Lemma Equation 7,…”

mentioning

confidence: 84%

“…Let us consider the first term in the summation of Equation 30. Using lemma 2, maximal inequality for reverse martingales Lee (1990, p.112), lemma 2.2 of Sen and Ghosh (1981), and lemma 7.3 of De and Chattopadhyay (2015), we have,…”

mentioning

confidence: 97%

See 3 more Smart Citations

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

Chattopadhyay¹,

Kelley

2016

Multivariate Behavioral Research

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The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.

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“…Proof. This proof is along the same lines as the proof of Lemma 7.7 of De and Chattopadhyay (2015). We note, (…”

mentioning

confidence: 70%

Section: Theoretical Resultsmentioning

confidence: 96%

mentioning

confidence: 84%

mentioning

confidence: 97%

See 2 more Smart Citations

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

Chattopadhyay¹,

Kelley

2016

Multivariate Behavioral Research

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“…Kanninen (1993); Greene (1998); Arcidiacono and Jones (2003); Aguirregabiria and Mira (2007) and many others contributed to application of sequential analysis in the field of economics, data analysis, medicine, and other areas. Recently, Chattopadhyay and De (2016) and De and Chattopadhyay (2017) developed a sequential procedure for inference problems related to the Gini index under independent and identically distributed (i.i.d.) conditions, but the proposed methodology cannot be used for finding a sufficiently narrow 100(1 − α)% confidence interval for the population Gini index under a complex household survey design.…”

Section: Introductionmentioning

confidence: 99%

Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data

2020

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The Gini index, a widely used economic inequality measure, is computed using data whose designs involve clustering and stratification, generally known as complex household surveys. Under complex household survey, we develop two novel procedures for estimating Gini index with a pre-specified error bound and confidence level. The two proposed approaches are based on the concept of sequential analysis which is known to be economical in the sense of obtaining an optimal cluster size which reduces project cost (that is total sampling cost) thereby achieving the pre-specified error bound and the confidence level under reasonable assumptions. Some large sample properties of the proposed procedures are examined without assuming any specific distribution. Empirical illustrations of both procedures are provided using the consumption expenditure data obtained by National Sample Survey (NSS) Organization in India.

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Estimating the standardized mean difference with minimum risk: Maximizing accuracy and minimizing cost with sequential estimation.

Chattopadhyay¹,

Kelley

2017

Psychological Methods

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The standardized mean difference is a widely used effect size measure. In this article, we develop a general theory for estimating the population standardized mean difference by minimizing both the mean square error of the estimator and the total sampling cost. Fixed sample size methods, when sample size is planned before the start of a study, cannot simultaneously minimize both the mean square error of the estimator and the total sampling cost. To overcome this limitation of the current state of affairs, this article develops a purely sequential sampling procedure, which provides an estimate of the sample size required to achieve a sufficiently accurate estimate with minimum expected sampling cost. Performance of the purely sequential procedure is examined via a simulation study to show that our analytic developments are highly accurate. Additionally, we provide freely available functions in R to implement the algorithm of the purely sequential procedure. (PsycINFO Database Record

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Minimum Risk Point Estimation of Gini Index

Cited by 9 publications

References 24 publications

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data

Estimating the standardized mean difference with minimum risk: Maximizing accuracy and minimizing cost with sequential estimation.

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