Widening the Applicability of Confidence Interval Methods: The Propagating Imprecision Approach

This paper evaluates the use of several known simultaneous confidence interval methods for the automated recognition of handwritten digits from data in a well-known handwriting database. Contained in this database are handwritten digits, 0 through 9, that were obtained from 42,000 participants' writing samples. The objective of the analyses is to utilize statistical testing procedures that can be easily automated by a computer to recognize which digit was written by a subject. The methodologies discussed in this paper are designed to be sensitive to Type I errors and will control an overall measure of these errors, called the Familywise Error Rate. The procedures were constructed based off of a training portion of the data set, then applied and validated on the remaining testing portion of the data.

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A new framework of statistical inferences based on the valid joint sampling distribution of the observed counts in an incomplete contingency table

Statistical Methods in Medical Research ◽

10.1177/0962280215586591 ◽

2015 ◽

Vol 26 (4) ◽

pp. 1712-1736 ◽

Cited By ~ 1

Author(s):

Guo-Liang Tian ◽

Hui-Qiong Li

Keyword(s):

Confidence Interval ◽

Contingency Table ◽

Contingency Tables ◽

Sampling Distribution ◽

Maximum Likelihood Estimates ◽

Interval Methods ◽

Simulation Studies ◽

Underlying Assumption ◽

Incomplete Observations ◽

New Framework

Some existing confidence interval methods and hypothesis testing methods in the analysis of a contingency table with incomplete observations in both margins entirely depend on an underlying assumption that the sampling distribution of the observed counts is a product of independent multinomial/binomial distributions for complete and incomplete counts. However, it can be shown that this independency assumption is incorrect and can result in unreliable conclusions because of the under-estimation of the uncertainty. Therefore, the first objective of this paper is to derive the valid joint sampling distribution of the observed counts in a contingency table with incomplete observations in both margins. The second objective is to provide a new framework for analyzing incomplete contingency tables based on the derived joint sampling distribution of the observed counts by developing a Fisher scoring algorithm to calculate maximum likelihood estimates of parameters of interest, the bootstrap confidence interval methods, and the bootstrap testing hypothesis methods. We compare the differences between the valid sampling distribution and the sampling distribution under the independency assumption. Simulation studies showed that average/expected confidence-interval widths of parameters based on the sampling distribution under the independency assumption are shorter than those based on the new sampling distribution, yielding unrealistic results. A real data set is analyzed to illustrate the application of the new sampling distribution for incomplete contingency tables and the analysis results again confirm the conclusions obtained from the simulation studies.

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