References

Here you find an overview of the literature about constrained statistical Inference, robust estimation or a combination of both. All formulas used in restriktor are coming from these articles.

Barlow, R. E., D. J. Bartholomew, H. M. Bremner, and H. D. Brunk. 1972. Statistical Inference Under Order Restrictions. New York: Wiley.

Bartholomew, D.J. 1959a. “A Test of Homogeneity for Ordered Alternatives.” Biometrika 46: 36–48.

———. 1959b. “A Test of Homogeneity for Ordered Alternatives. II.” Biometrika 46: 328–35.

———. 1961a. “A Test of Homogeneity of Means Under Restricted Alternatives.” Journal of the Royal Statistical Society. Series B (Methodological) 23: 239–81.

———. 1961b. “Ordered Tests in the Analysis of Variance.” Biometrika 48: 325–32.

Dykstra, R. 1991. “Asymptotic Normality for Chi-Bar-Square Distributions.” The Canadian Journal of Statistics 19: 297–306.

Efron, E., and R.J. Tibshirani. 1993. An Introduction to the Bootstrap. Chapman & Hall.

Gouriéroux, C., A. Holly, and A. Monfort. 1982. “Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters.” Econometrica 50: 63–80.

Grömping, U. 2010. “Inference with Linear Equality and Inequality Constraints Using R: The Package Ic.infer.” Journal of Statistical Software 33: 1–31. doi:10.18637/jss.v033.i10.

Hampel, F., Ronchetti E., Rousseeuw P., and W. Stahel. 1986. Robust Statistics. John Willey; Sons, New York.

Huber, P.J. 1964. “Robust Estimation of a Location Parameter.” The Annals of Mathematical Statistics 35: 73–101.

———. 1973. “Robust Regression: Asymptotics, Conjectures and Monte Carlo.” The Annals of Statistics 1: 799–821.

———. 1981. Robust Statistics. New York: Wiley.

Huber, P.J., and E.M. Ronchetti. 2009. Robust Statistics. New York: Wiley.

Kudô, A. 1963. “A Multivariate Analogue of the One-Sided Test.” Biometrika 50: 403–18.

Kudô, A., and J.R. Choi. 1975. “A Generalized Multivariate Analogue of the One Sided Test.” Memoirs of the Faculty of Science 29: 303–28.

Kuiper, R.M., H. Hoijtink, and M.J. Silvapulle. 2011. “Generalization of the Order-Restricted Information Criterion for Multivariate Normal Linear Models.” Biometrica 2: 495–501.

Kuiper, R.M., I.G. Klugkist, and H.J.A. Hoijtink. 2010. “A Fortran 90 Program for Confirmatory Analysis of Variance.” Journal of Statistical Software 34: 1–31.

Nüesch, P.E. 1966. “On the Problem of Testing Location in Multivariate Populations for Restricted Alternatives.” The Annals of Mathematical Statistics 37: 113–9.

Perlman, M.D. 1969. “One-Sided Testing Problems in Multivariate Analysis.” The Annals of Mathematical Statistics 40: 549–67.

Robertson, T., F. T. Wright, and R. L. Dykstra. 1988. Order Restricted Statistical Inference. New York: Wiley.

Rousseeuw, P., and V. Yohai. 1984. “Robust Regression by Means of S-Estimators.” In Robust and Nonlinear Time Series Analysis, edited by J. Franke, W. Härdle, and D. Martin, 256–72. Spring-Verlag: New York.

Salibián-Barrera, M. 2005. “Estimating the p-Values of Robust Tests for the Linear Model.” Journal of Statistical Planning and Inference 128: 241–57. doi:doi:10.1016/j.jspi.2003.09.033.

Salibián-Barrera, M., S. Van Aelst, and V.J. Yohai. 2014. “Robust Tests for Linear Regression Models Based on τ-Estimates.” Computational Statistics and Data Analysis. doi:10.1016/j.csda.2014.09.012v.

Schoenberg, R. 1997. “Constrained Maximum Likelihood.” Computational Economics 10: 251–66.

Schrader, R.M., and T.P. Hettmansperger. 1980. “Robust Analysis of Variance Based Upon a Likelihood Ratio Criterion.” Biometrika 67: 93–101.

Self, S.G., and K.Y. Liang. 1987. “Asymptotic Properties of Maximum Likelihood Estimators and the Likelihood Ratio Tests Under Nonstandard Conditions.” Journal of the American Statistical Association, no. 82: 605–10.

Shapiro, A. 1988. “Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis.” International Statistical Review, 49–62. doi:10.2307/1403361.

Shi, N.Z., S.R. Zheng, and J. Guo. 2005. “The Restricted EM Algorithm Under Inequality Restrictions on the Parameters.” Journal of Multivariate Analysis, no. 92: 53–76.

Silvapulle, M. 1992a. “Robust Tests of Inequality Constraints and One-Sided Hypotheses in the Linear Model.” Biometrika 79: 621–30.

———. 1992b. “Robust Wald-Type Tests of One-Sided Hypotheses in the Linear Model.” Journal of the American Statistical Association 87 (417): 156–61.

———. 1996a. “On an F-type Statistic for Testing One-Sided Hypotheses and Computation of Chi-Bar-Squared Weights.” Statistics & Probability Letters 28: 137–41.

———. 1996b. “Robust Bounded Influence Tests Against One-Sided Hypotheses in General Parametric Models.” Statistics & Probability Letters, no. 31: 45–50.

———. 1997. “On Order Restricted Inference in Some Mixed Linear Models.” Statistics & Probability Letters 36: 23–27.

Silvapulle, M., and P. Silvapulle. 1995. “A Score Test Against One-Sided Alternatives.” American Statistical Association 90 (429): 342–49.

Silvapulle, M.J. 1994. “On Tests Against One-Sided Hypotheses in Some Generalized Linear Models.” Biometrics, no. 50: 853–58.

Silvapulle, M.J., and P.K. Sen. 2005. Constrained Statistical Inference: Order, Inequality, and Shape Constraints. Hoboken, NJ: Wiley.

Vanbrabant, L., R. Van de Schoot, and Y Rosseel. 2015. “Constrained Statistical Inference: Sample-Size Tables for ANOVA and Regression.” Frontiers in Psychology 5: 1–8. doi:10.3389/fpsyg.2014.01565.

Wolak, F. 1987. “An Exact Test for Multiple Inequality and Equality Constraints in the Linear Regression Model.” Journal of the American Statistical Association 82 (399): 782–93.

Wolak, F.A. 1989. “Testing Inequality Constraints in Linear Econometric Models.” Journal of Econometrics 41: 205–35.

Wright, F.T. 1988. “The One-Way Analysis of Variance with Ordered Alternatives: A Modification of Bartholomew’s $\bar{E}^2$ Test.” The Canadian Journal of Statistics.

Yancey, T.A., G.G. Judge, and M.E. Bock. 1981. “Testing Multiple Equality and Inequality Hypothesis Is Economics.” Economics Letters 7: 249–55.

Yohai, V.J. 1987. “High Breakdown-Point and High Efficiency Robust Estimates for Regression.” The Annals of Statistics 15: 642–56.

Zelazo, P.R., N.A. Zelazo, and S. Kolb. 1972. “‘Walking’ in the Newborn.” Science.