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Course detail
FSI-SP3Acad. year: 2024/2025
This course is concerned with the following topics: theory of estimation, maximum likelihood, method of moments, Bayesian methods of estimation, testing statistical hypotheses, nonparametric methods, exponential family of distribution, asymptotic tests, generalized linear models.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Aims
Students acquire needed knowledge from important parts of mathematical statistics, which will enable them to evaluate and develop stochastic models of technical phenomena and processes based on these methods and use them on PC.
Study aids
Prerequisites and corequisites
Basic literature
Recommended literature
Classification of course in study plans
specialization CZS , 1 year of study, winter semester, elective
Lecture
Teacher / Lecturer
Syllabus
Unbiased and consistent estimatesRegular family of distributions, Rao - Cramér theorem, efficient estimatesFisher information and Fisher information matrixSufficient statistics, Neuman factorization criterionRao - Blackwell theorem and its applications Method of moments, maximum likelihood methodBayesian approachTesting statistical hypothesesPrinciples of nonparametric methodsExponential family of distributionAsymptotic tests based on likelihood functionTests with nuisance parameters, examplesTests of hypotheses on parametersGeneralized linear models
Computer-assisted exercise
Unbiased and consistent estimates - examples of estimates and verification of their propertiesComputation of the lower bound for variance of unbiased estimatesDetermination of Fisher information and Fisher information matrix for given distributionsApplications of Neuman factorization criterionFindings estimates by Rao - Blackwell theorem Estimator’s determination by method of moments and by maximum likelihood method Estimator’s determination by Bayes methodPowers of test and derivation of uniformly most powerful testsApplication of nonparametric methos in data analysisVerification of exponential family for a given distributionApplication of asymptotic tests based on likelihood functionTests with nuisance parameters, estimates of parameters for Weibull and gamma distributionTests of hypotheses on parameters of generalized linear model