Bayesian empirical likelihood methods for quantile comparisons

다국어 초록 (Multilingual Abstract)

Bayes factors, practical tools of applied statistics, have been dealt with extensively in the literature in the context of hypothesis testing. The Bayes factor based on parametric likelihoods can be considered both as a pure Bayesian approach as well as a standard technique to compute p-values for hypothesis testing. We employ empirical likelihood methodology to modify Bayes factor type procedures for the nonparametric setting. The paper establishes asymptotic approximations to the proposed procedures. These approximations are shown to be similar to those of the classical parametric Bayes factor approach. The proposed approach is applied towards developing testing methods involving quantiles, which are commonly used to characterize distributions.Wepresent and evaluate one and two sample distribution free Bayes factor type methods for testing quantiles based on indicators and smooth kernel functions. An extensive Monte Carlo study and real data examples show that the developed procedures have excellent operating characteristics for one-sample and two-sample data analysis.

참고문헌 (Reference)

1 Wilks, S. S., "Weighting systems for linear functions of correlated variables when there is no dependent variable" 3 : 23-40, 1938

2 Zilberberg, M. D., "Ventilator-associated pneumonia: the clinical pulmonary infection score as a surrogate for diagnostics and outcome" 51 : S131-S135, 2010

3 Yu, J., "Two-sample empirical likelihood ratio tests for medians in application to biomarker evaluations" 39 : 671-689, 2011

4 Krieger, A. M., "Surveillance of a simple linear regression" 98 : 456-469, 2003

5 Berger, J. O, "Statistical decision theory and Bayesian analysis" Springer 1985

6 Nadaraya, E., "Some new estimates for distribution functions" 9 : 497-500, 1964

7 Chen, S. -X., "Smoothed empirical likelihood confidence intervals for quantiles" 21 : 1166-1181, 1993

8 Freidlin, B., "Should the median test be retired from general use?" 54 : 161-164, 2000

9 Monahan, J. F., "Proper likelihoods for bayesian analysis" 79 : 271-278, 1992

10 Vexler, A., "Optimal hypothesis testing : from semi to fully bayes factors" 71 : 125-138, 2010

11 Mood, A. M., "On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests" 25 : 514-522, 1954

12 Vexler, A., "Modifications of the empirical likelihood interval estimation with improved coverage probabilities" 38 : 2171-2183, 2009

13 Erkanli, A., "Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space" 89 : 250-258, 1994

14 Marden, J. I., "Hypothesis testing : from p values to bayes factors" 95 : 1316-1320, 2000

15 Owen, A. B., "Empirical likelihood ratio confidence intervals for a single functional" 75 : 237-249, 1988

16 Lazar, N. A., "Empirical likelihood in the presence of nuisance parameters" 86 : 203-211, 1999

17 Yu, J., "Empirical likelihood approaches to two-group comparisons of upper quantiles applied to biomedical data" 6 : 30-40, 2014

18 Qin, J., "Empirical likelihood and general estimating equations" 22 : 300-325, 1994

19 Owen, A. B., "Empirical likelihood" Chapman & Hall/CRC 2001

20 Vexler, A., "Data-driven confidence interval estimation incorporating prior information with an adjustment for skewed data" 70 : 243-249, 2016

21 Wilcox, R. R., "Comparing two independent groups via multiple quantiles" 44 : 91-99, 1995

22 Doss, H., "Bayesian nonparametric estimation of the median; part II : asymptotic properties of the estimates" 13 : 1445-1464, 1985

23 Doss, H., "Bayesian nonparametric estimation of the median; part I : computation of the estimates" 13 : 1432-1444, 1985

24 Gelfand, A. E., "Bayesian model choice: asymptotics and exact calculations" 56 : 501-514, 1994

25 Carlin, B. P., "Bayesian methods for data analysis" Chapman & Hall/CRC 2008

26 Lazar, N. A., "Bayesian empirical likelihood" 90 : 319-326, 2003

27 Kass, R. E, "Bayes factors in practice" 42 : 551-560, 1993

28 Kass, R. E., "Bayes factors" 90 : 773-795, 1995

29 Bleistein, N., "Asymptotic expansions of integrals" Ardent Media 1975

30 Serfling, R. J., "Approximation theorems of mathematical statistics" Weiley 1981

31 Davison, A. C., "Approximate predictive likelihood" 73 : 323-332, 1986

32 Kass, R. E., "Approximate bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions" 54 : 129-144, 1992

33 Yu, J., "Analyzing incomplete data subject to a threshold using empirical likelihood methods : An application to a pneumonia risk study in an icu setting" 66 : 123-130, 2009

34 Hughes, M. D., "Analysis and design issues for studies using censored biomarker measurements with an example of viral load measurements in hiv clinical trials" 19 : 3171-3191, 2000

35 Vexler, A., "An optimal retrospective change point detection policy" 36 : 542-558, 2009

36 Hutson, A. D., "An exact two-group median test with an extension to censored data" 19 : 103-112, 2007

37 Zhou, W., "Adjusted empirical likelihood method for quantiles" 55 : 689-703, 2003

38 Tierney, L., "Accurate approximations for posterior moments and marginal densities" 81 : 82-86, 1986

39 Scannapieco, F. A., "A randomized trial of chlorhexidine gluconate on oral bacterial pathogens in mechanically ventilated patients" 13 : R117-, 2009

40 Azzalini, A., "A note on the estimation of a distribution function and quantiles by a kernel method" 68 : 326-328, 1981

41 Kass, R. E., "A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion" 90 : 928-934, 1995