Probability estimation when some observations are grouped

Abstract

This paper considers the use of additional questions for decreasing survey non-response rates and an approach for estimating a probability based on the results obtained. In a survey, the respondents are asked to answer an original question and follow-up questions, where the answers for the follow-up questions are grouped answers for the original question. For example, respondents are asked to provide an exact number of incidents, but in cases of 'Do not know' or 'Refuse' responses, they are subsequently asked to pick an answer from a less specific categorical scale. The new estimator obtains smaller variance asymptotically and does not depend on a distribution family. This method is applied to income questions in a survey regarding injury prevention and behaviours. Another application is survey data on intimate partner violence, where some amendments were applied for incorporating post-stratification weights and for using non-random grouping. For additional illustration, an example of parameter estimation on artificially generated data is presented.

Use of Uncertain External Information in Statistical Estimation

“…This section presents the main statistical formulas regarding the use of external information proposed in [4,5] (variance minimization), and [8,20] (MSE minimization) and applies these methods to Walmart sales data.…”

“…In [4], Tarima and Pavlov propose a method for incorporating uncertain external information in statistical estimation. [4] and [5] postulate the unbiasedness of additional information. This, for example, means that in different stores the expected sales are the same.…”

Coping with Information Loss and the Use of Auxiliary Sources of Data: A Report from the NISS Ingram Olkin Forum Series on Unplanned Clinical Trial Disruptions

“…Some researchers have explored the use of auxiliary information available in the form of known population quantities, see Zenkova and Krainova (2017); Dmitriev et al (2014); others have used auxiliary information available in form of summary statistics such as sample means and standard errors, see Tarima and Pavlov (2006); Tarima et al (2007). Asymptotic relative efficiency of the estimators proposed in Tarima and Pavlov (2006) is derived in Albertus (2022).…”

Use of Uncertain Additional Information in Newsvendor Models

“…This approach assumed that the additional information is unbiased, meaning that averaged sales for both stores are about the same. A similar assumption was made in [8]. It is possible that additional information can be biased, then minimum mean squared error (MSE) can be considered instead [9], [10].…”