Derivation of Monotone Likelihood Ratio Using Two Sided Uniformly Normal Distribution Techniques
In this paper, two-sided uniformly normal distribution techniques were used in the derivation of monotone likelihood ratio. The approach mainly employed the parameters of the distribution for a class of all size a. The derivation technique is fast, direct and less burdensome when compared to some existing methods.
<p>[1] Commenges, D. , Sayyareh, A., letenneur, L. , Guedj, J, and Bar-hen, A, (2008), “Estimating a Difference of Kullback-Leibler Risks Using a Normalized Difference of AIC’’, The Annals of Applied Statistics, Vol. 2,No. 3, pp.1123 -1142.
[2] Cox, D.R. (1961), “Test of Separate Families of Hypothesis’’, Proceeding of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol.1, pp.105 – 123.
[3] Cox, D.R.” (1962), Further Result on Tests of Separate Families of Hypotheses’’, Journal of the Royal Statistical Society, Vol. B, No. 24 pp.406 – 424.
[4] Fisher, R.A. (1922), “On the mathematical foundations of theoretical statistics”, Philosophical Transactions of the Royal Society Vol. A, No.222. pp.309 – 3689.
[5] Fisher, R.A. (1955), “Statistical Methods and Scientific Induction’’, Journal of the Royal Statistical Society, (1989), Vol. B, No. 17, pp.69 – 78.
[6] Fisher, G. and McAleer, M. (1981), “Alternative Procedures and Associated Tests of Significance for Non-Nested Hypotheses”, Journal of Econometrics, Vol. 16, pp.103 – 119.
[7] Lehmann, E.L., (1986). “Testing Statistical Hypotheses” New York, John Wiley, II edition.
[8] Neyman, J. (1956), “Note on an article by Sir Ronald Fisher”, Journal of the Royal Statistical Society, Vol. B, No. 18, pp.288 – 294.
[9] Sayyareh, A., Obeidi, R., and Bar-hen, A. (2011), “Empirical comparison of some model selection criteria”, Communication in Statistics Simulation and Computation, Vol.40 pp.72 – 86.
[10] Sayyareh, A., Barmalzan G., and Haidari, A, (2011), “Two Sided Uniformly most powerful test for Pitman Family”, Applied Mathematical Sciences Vol. 5, No.74, pp.3649 – 3660.
[11] Vuong, Q.H. (1989), “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses”, Econometrica, Vol. 57, No. 2, 307 – 333.</p>
<p>[1] Commenges, D. , Sayyareh, A., letenneur, L. , Guedj, J, and Bar-hen, A, (2008), “Estimating a Difference of Kullback-Leibler Risks Using a Normalized Difference of AIC’’, The Annals of Applied Statistics, Vol. 2,No. 3, pp.1123 -1142.
[2] Cox, D.R. (1961), “Test of Separate Families of Hypothesis’’, Proceeding of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol.1, pp.105 – 123.
[3] Cox, D.R.” (1962), Further Result on Tests of Separate Families of Hypotheses’’, Journal of the Royal Statistical Society, Vol. B, No. 24 pp.406 – 424.
[4] Fisher, R.A. (1922), “On the mathematical foundations of theoretical statistics”, Philosophical Transactions of the Royal Society Vol. A, No.222. pp.309 – 3689.
[5] Fisher, R.A. (1955), “Statistical Methods and Scientific Induction’’, Journal of the Royal Statistical Society, (1989), Vol. B, No. 17, pp.69 – 78.
[6] Fisher, G. and McAleer, M. (1981), “Alternative Procedures and Associated Tests of Significance for Non-Nested Hypotheses”, Journal of Econometrics, Vol. 16, pp.103 – 119.
[7] Lehmann, E.L., (1986). “Testing Statistical Hypotheses” New York, John Wiley, II edition.
[8] Neyman, J. (1956), “Note on an article by Sir Ronald Fisher”, Journal of the Royal Statistical Society, Vol. B, No. 18, pp.288 – 294.
[9] Sayyareh, A., Obeidi, R., and Bar-hen, A. (2011), “Empirical comparison of some model selection criteria”, Communication in Statistics Simulation and Computation, Vol.40 pp.72 – 86.
[10] Sayyareh, A., Barmalzan G., and Haidari, A, (2011), “Two Sided Uniformly most powerful test for Pitman Family”, Applied Mathematical Sciences Vol. 5, No.74, pp.3649 – 3660.
[11] Vuong, Q.H. (1989), “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses”, Econometrica, Vol. 57, No. 2, 307 – 333.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65479", author = "D. A. Farinde", title = "Derivation of Monotone Likelihood Ratio Using Two Sided Uniformly Normal Distribution Techniques", abstract = "In this paper, two-sided uniformly normal distribution techniques were used in the derivation of monotone likelihood ratio. The approach mainly employed the parameters of the distribution for a class of all size a. The derivation technique is fast, direct and less burdensome when compared to some existing methods.
", keywords = "Neyman-Pearson Lemma, Normal distribution", volume = "7", number = "10", pages = "1544-5", }
