Syllabus
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Course Code: ST-302 Course Name: Inference-II |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Elements of Statistical decision theory. Neyman - Pearson lemma (with emphasis on the motivation of theory of testing of hypothesis) BCR and sufficient statistics.Testing a simple hypothesis against a class of alternatives. Most powerful test, Uniformly most powerful test and sufficient statistics, power function. One and two sided tests. |
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| 2 | Composite hypotheses, An optimum property of sufficient statistics. Similar regions, Elementary ideas of complete statistics, Completeness of sufficient statistics.Likelihood ratio test and its applications, asymptotic distribution of LR statistic and asymptotic power of LR tests.Sequential Analysis. Concept of ASN and OC functions. Wald's sequential probability ratio test and its OC and ASN functions.Distribution of order statistics and range. |
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| 3 | Non - parametric tests and their applications: Empirical distribution function and its properties(without Proof), Test of randomness (Test based on the total number of runs). One- sample and paired-sample techniques: The Ordinary Sign test and Wilcoxon Signed-rank test. Tests of Goodness of Fit: Chi-square Goodness of Fit, The Empirical distribution function, Kolmogrov- Smirnov tests, Independence in Bivariate sample: Kendall’s Tau coefficient and Spearman’s rankcorrelation. |
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| 4 | Generalized two-sample problem: The Wald-Wolfowitz Runs test, Kolmogrov-Smirnov two sample Test, Median Test, Mann-Whitney U Test, Linear Ranked tests for the Location and Scale problem: Wilcoxon Test, Mood Test, Siegel-Tukey Test, Klotz Normal-scores Test, Sukhatme Test.Kruskalwallis ANOVA test, Concept of Jackknife, Bootstrap methods. |
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