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Semiparametric Inference for the Two-way Layout Under Order Restrictions

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  • OrI Davidov
  • Konstantinos Fokianos
  • George Iliopoulos

Abstract

type="main" xml:id="sjos12052-abs-0001"> There are many situations in which a researcher would like to analyse data from a two-way layout. Often, the assumptions of linearity and normality may not hold. To address such situations, we introduce a semiparametric model. The model extends the well-known density ratio model from the one-way to the two-way layout and provides a useful framework for semiparametric analysis of variance type problems under order restrictions. In particular, the likelihood ratio order is emphasized. The model enables highly efficient inference without resorting to fully parametric assumptions or the use of transformations. Estimation and testing procedures under order restrictions are developed and investigated in detail. It is shown that the model is robust to misspecification, and several simulations suggest that it performs well in practice. The methodology is illustrated using two data examples; in the first, the response variable is discrete, whereas in the second, it is continuous.

Suggested Citation

  • OrI Davidov & Konstantinos Fokianos & George Iliopoulos, 2014. "Semiparametric Inference for the Two-way Layout Under Order Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 622-638, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:622-638
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    File URL: http://hdl.handle.net/10.1111/sjos.12052
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    References listed on IDEAS

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    1. Konstantinos Fokianos & Irene Kaimi, 2006. "On the Effect of Misspecifying the Density Ratio Model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 475-497, September.
    2. Ori Davidov & Konstantinos Fokianos & George Iliopoulos, 2010. "Order-Restricted Semiparametric Inference for the Power Bias Model," Biometrics, The International Biometric Society, vol. 66(2), pages 549-557, June.
    3. Zhang, Biao, 2002. "Assessing Goodness-of-Fit of Generalized Logit Models Based on Case-Control Data," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 17-38, July.
    4. Konstantinos Fokianos, 2004. "Merging information for semiparametric density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 941-958, November.
    5. Christopher A. Carolan & Joshua M. Tebbs, 2005. "Nonparametric tests for and against likelihood ratio ordering in the two-sample problem," Biometrika, Biometrika Trust, vol. 92(1), pages 159-171, March.
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    1. Mondal, Anjana & Sattler, Paavo & Kumar, Somesh, 2023. "Testing against ordered alternatives in a two-way model without interaction under heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Heng Wang & Ping-Shou Zhong, 2017. "Order-restricted inference for means with missing values," Biometrics, The International Biometric Society, vol. 73(3), pages 972-980, September.
    3. Bogomolov, Marina & Davidov, Ori, 2019. "Order restricted univariate and multivariate inference with adjustment for covariates in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 20-27.
    4. Belmiro P. M. Duarte & Anthony C. Atkinson & Satya P. Singh & Marco S. Reis, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," Statistical Papers, Springer, vol. 64(2), pages 587-615, April.
    5. Duarte, Belmiro P.M. & Atkinson, Anthony C. & P. Singh, Satya & S. Reis, Marco, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," LSE Research Online Documents on Economics 115187, London School of Economics and Political Science, LSE Library.

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