Estimation of Gini Index within Pre-Specied Error Bound

Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size methods cannot simultaneously achieve both the specified confidence coefficient and specified width. We develop a purely sequential procedure for interval estimation of Gini index with a specified confidence coefficient and a fixed margin of error. Optimality properties of the proposed method, namely first order asymptotic efficiency and asymptotic consistency are proved. All theoretical results are derived without assuming any specific distribution of the data

Accuracy in insurance billing error estimation using auxiliary information

Billing fraud by health care providers is a widespread problem to a country’s health care system. This article develops a general theory for estimating the billing error in medical claims within pre-specified error bound using auxiliary information on the average payment amount made by all persons in the population. Estimation methods with pre-specified sample size cannot be used to achieve the fixed-width confidence interval for billing error. In this article we propose two two-stage procedures for accuracy in estimating billing error in medical claims using sample standard deviation and sample Gini’s mean difference as estimators of population standard deviation. This problem is the same as constructing a fixed-width confidence interval for billing error. In two-stage estimation procedures, the final sample size is not fixed in advance by using supposed unknown population parameter(s). Data in two-stage procedures are collected in two stages in which the final sample size is based on the estimate of the unknown parameter(s) in the first stage. The comparison of the proposed two-stage procedures are examined using a Monte Carlo simulation study

Estimation of location parameter within pre-specified error bound with second-order efficient two-stage procedure

This paper develops a general approach for constructing a confidence interval for a parameter of interest with a specified confidence coefficient and a specified width. This is done assuming known a positive lower bound for the unknown nuisance parameter and independence of suitable statistics. Under mild conditions, we develop a modified two-stage procedure which enjoys attractive optimality properties including a second-order efficiency property and asymptotic consistency property. We extend this work for finding a confidence interval for the location parameter of the inverse Gaussian distribution. As an illustration, we developed a modified mean absolute deviation-based procedure in the supplementary section for finding a fixed-width confidence interval for the normal mean

An Exploratory Study of the Role of Educational Incentives in Primary Education in Gujarat

This study explores the role of incentives—monetary or non-monetary compensation offered to children so that an educational need is fulfilled or perceived cost is brought down—in attaining certain expected educational enrolment and retention outcomes. It draws on a survey conducted in six villages in Gujarat. Incentives themselves may not be that critical in improving access and retention performance; other socio-economic and school-related factors may be more significant in ensuring access and retention. However, incentives may have help in keeping the poorer performers in school.

Performance of U-Statistics Having Kernels of Degree Higher Than Two in Inference Problems with Applications

This dissertation addresses some interesting inferential problems for the location and scale using the role of U-Statistics. It primarily focuses on using the U-statistics for estimating population standard deviation for the distributions where certain moments exist. We develope new test statistics for a one-sample problem which in some cases have better efficiency than the customary sign test. Next, we obtain percentile points of Gini\u27s mean difference (GMD) based test statistics which can be used for testing the population mean when observations come from a normal distribution with suspect outliers. ^ We implement the full spectrum of Hoeffding\u27s (1948, 1961) U-statistics for different inference problems. In the first case, we consider the unbiased estimation of a population standard deviation σ using GMD in the face of observing possible outliers when random samples arrive from a normal population. Nair (1936) proposed a suitable multiple of GMD that could be used to estimate a unbiasedly and explored its role with regard to robustness issues. ^ We introduce a technique based on U-statistics of higher orders, by modifying the GMD to come up with new unbiased estimators of σ. They are more efficient than the unbiased form of GMD. Next, we have indicated how a similar extension of the degree of a kernel for sample variance does not lead to a new estimator of σ2. In the process, we come up with an entirely new interpretation of S2. ^ This new technique is interesting in its own right and we demonstrate this by additionally constructing new competing nonparametric tests in the case of both one-sample and two-sample location problems. ^ We have provided the percentile points of GMD based test statistics which can be utilized for testing the mean when observations come from a normal distribution with suspect outliers and have successfully implemented our methodology on a realistic dataset. ^ We conclude that the newly developed methodologies have worked remarkably well, both theoretically as well as practically. Such methodologies are rich enough to feed into a wide range of future research problems of practical significance.

Regional reporting of the incidence of Anaplastic Lymphoma Kinase mutation in 379 non-small-cell lung cancer patients from Kolkata: Using immunohistochemistry as the diagnostic modality in a significant subset

Context: Regional epidemiology of anaplastic lymphoma kinase (ALK) mutation in non-small-cell lung cancer (NSCLC) is an unmet need in India, and so is the knowledge of its incidence based on immunohistochemistry (IHC). Aims: Reporting the incidence of ALK mutation in NSCLC from Kolkata, incorporating IHC as the diagnostic modality in a considerable subset of patients. Subjects and Methods: It is a retrospective observational study done on NSCLC patients with adenocarcinoma histology, unselected by epidermal growth factor receptor, whose samples were tested for ALK mutation status between March 1, 2013, and March 15, 2017. The study involved all cancer facilities in Kolkata, except Tata Medical Centre. Up to June 2015, the tests were done by fluorescence in situ hybridization (FISH) and from July 2015 to the end, tests were done using IHC, as per the standard testing guidelines existing during the respective time periods. Results were documented in a de-identified manner to analyze the incidence of ALK mutations. Results: A total of 379 patients was tested for ALK mutations. March 2013 to June 2015, 200 (52.77%) patients were tested by FISH, 17 (8.5%) samples were unreportable and 4 patients [(2.19%) 4/183] tested positive for ALK mutations. From July 2015 to March 2017, 179 (47.22%) patients were tested by IHC, 9 (5.02%) samples were unreportable, and 10 patients [(5.88%) 10/170] tested positive for ALK mutations. Overall, 26 (6.8%) samples were unreportable and 14 [(3.9%) 14/353] patients tested positive for ALK mutations. Conclusions: The overall incidence of ALK mutation positive NSCLC in Kolkata is 3.9%. The incidence by IHC is 5.88% and by FISH is 2.19%, in the subset of patients tested by these two modalities respectively

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

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

Estrogen receptor and progesterone receptor status of breast cancer patients of eastern India: A multi-institutional study

Context: There is a paucity of any significant data on the estrogen receptor (ER) and progesterone receptor (PR) status of breast cancer patients from the eastern part of India. Aims: This study aims to document the ER and PR status of breast cancer patients in the eastern Indian population, as catered by two premier tertiary care hospitals in Kolkata. Subjects and Methods: All breast cancer patients registered between January 1, 2013 and December 31, 2015, in the Departments of Oncology, of IPGMER and SSKM Hospitals and R. G. Kar Medical College and Hospital, Kolkata, who had at least undergone a core biopsy or surgery, were analyzed retrospectively for documentation of their ER and PR status, using the 2010 American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) interpretation guidelines. Results: Over a period of 3 years, a total of 927 patients were included for the study. A total of 825 (89%) patients had their ER and PR data available for evaluation. ER and PR positive was seen in 312 (37.82%) patients, ER and PR negative in 399 (48.36%) patients, ER positive and PR negative in 71 (8.6%) patients, and ER negative and PR positive results was found in 43 (5.21%) patients. Conclusions: This is the first multi-institutional documentation of ER and PR status from eastern India, having a modest number of patients and one of the earliest documentations using the latest ASCO/CAP interpretation guidelines. These findings resemble the data from the south and also reiterate the fact that majority of the Indian breast cancer patients are still ER and PR negative in spite of the changes in the interpretation guidelines