Yao and Tritchler (1993, Biometrics 49, 233-236) proposed an exact test for conditional independence in a series of 2 x 2 tables, and presented a fast Fourier transform (FFT) algorithm to compute exact significance le...
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Yao and Tritchler (1993, Biometrics 49, 233-236) proposed an exact test for conditional independence in a series of 2 x 2 tables, and presented a fast Fourier transform (FFT) algorithm to compute exact significance levels for it. The purpose of this note is to provide a general perspective on computational methods applicable to this problem. We also assess the power and efficiency comparisons done by them.
The field of exact analysis of independent discrete outcomes data with covariates has come of age in the recent years. Development of efficient numerical algorithms has been the prime factor fueling the growth. Exact ...
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The field of exact analysis of independent discrete outcomes data with covariates has come of age in the recent years. Development of efficient numerical algorithms has been the prime factor fueling the growth. Exact inference on correlated or time-varying discrete data, on the other hand, has garnered little attention. In this paper, we lay the foundation for exact analysis for one class of longitudinal data problems - Markov chain models with covariates. In particular, we focus on a two-state first-order stationary Markov chain model with a multi-level stratification factor and a binary covariate of interest. We show that exact distributions for such models derive from conditional convolutions of elemental Bose-Einstein distributions. We develop a recursive polynomial multiplication algorithm with checks for infeasibility to compute such distributions, and empirically demonstrate its efficiency. We utilize the algorithm to compare exact inference on Markov chain data with the traditional large sample method. Given the transition counts, the latter method is insensitive as to whether the data are generated from a few long chains or many short chains. The exact method takes this feature into account. Our findings point towards a potential problem with large sample inference, namely the use of observed instead of expected information in finite samples. This issue needs further study. It is also seen that with Markov chain data, inferences drawn from the exact method may differ from that from the asymptotic method at transition count values that may not be deemed small. (C) 1999 Elsevier Science B.V. All rights reserved.
Multinomial goodness-of-fit tests arise in a diversity of milieu. The long history of the problem has spawned a multitude of asymptotic tests. If the sample size relative to the number of categories is small, the accu...
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Multinomial goodness-of-fit tests arise in a diversity of milieu. The long history of the problem has spawned a multitude of asymptotic tests. If the sample size relative to the number of categories is small, the accuracy of these tests is compromised. In that case, an exact test is a prudent option. But such tests are computationally intensive and need efficient algorithms. This paper gives a conceptual overview, and empirical comparisons of two avenues, namely the network and fast Fourier transform (FFT) algorithms, for an exact goodness-of-fit test on a multinomial. We show that a recursive execution of a polynomial product forms the basis of both these approaches. Specific details to implement the network method, and techniques to enhance the efficiency of the FFT algorithm are given. Our empirical comparisons show that For exact analysis with the chi-square and likelihood ratio statistics, the network-cum-polynomial multiplication algorithm is the more efficient and accurate of the two.
The investigation of interaction in a series of 2 × 2 tables is warranted in a variety of research endeavors. Though many large-sample approaches for such investigations are available, the exact analysis of the p...
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