Ali-Akbar Haghdoost, Hossein Hessari, Mohammad Reza Baneshi, Maryam Rad, Arash Shahravan
The impact of mother's literacy on child dental caries: Individual data or aggregate data analysis?
Journal of education and health promotion
note chapter concludes problems complements notes references 1 statistical models goals performance criteria data models parameters statistics bayesian models decision theoretic framework prediction sufficiency exponential families 2 methods estimation basic heuristics estimation minimum contrast estimates estimating equations maximum likelihood multiparameter exponential families algorithmic issues 3 measures performance introduction bayes procedures minimax procedures unbiased estimation risk inequalities nondecision theoretic criteria 4 testing confidence regions introduction choosing test statistic neymanpearson lemma uniformly powerful tests monotone likelihood ratio models confidence bounds intervals regions duality confidence regions tests uniformly accurate confidence bounds frequentist bayesian formulations prediction intervals likelihood ratio procedures 5 asymptotic approximations introduction meaning uses asymptotics consistency first higherorder asymptotics delta method applications asymptotic theory one dimension asymptotic behavior optimality posterior distribution 6 inference multiparameter case inference gaussian linear models asymptotic estimation theory p dimensions large sample tests confidence regions large sample methods discrete data generalized linear models robustness properties semiparametric models appendix review basic probability theory basic model elementary properties probability models discrete probability models conditional probability independence compound experiments bernoulli multinomial trials sampling without replacement probabilities euclidean space random variables vectors transformations independence random variables vectors expectation random variable moments moment cumulant generating functions classical discrete continuous distributions modes convergence random variables limit theorems limit theorems inequalities poisson process appendix b additional topics probability analysis conditioning random variable vector distribution theory transformations random vectors distribution theory samples normal population bivariate normal distribution moments random vectors matrices multivariate normal distribution convergence random vectors op op notation multivariate calculus convexity inequalities topics matrix theory elementary hilbert space theory appendix c tables standard normal distribution auxiliary table standard normal distribution distribution critical values x 2 distribution critical values f distribution critical values index