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A unified approach to all problems of prediction, estimation, and hypothesis testing. It is based on concept of the decision function, which tells the performer of experiment how to conduct the statistical aspects of an experiment and which action to take for each possible outcome. Choosing the decision function needs a loss function to be defined which assigns numerical values to making bad or good decisions. Explicitly a general loss function is denoted by L d; expressing how bad it would be to make decision d if the parameter value were. A quadratic loss function, it could be defined as and a bilinear loss function as
Bimodal distribution : The probability distribution, or we can simply say the frequency distribution, with two modes. Figure 15 shows the example of each of them
The method or technique for producing the sequence of parameter estimates that, under the mild regularity conditions, converges to maximum likelihood estimator. Of particular signi
The Expectation/Conditional Maximization Either algorithm which is the generalization of ECM algorithm attained by replacing some of the CM-steps of ECM which maximize the constrai
1. You are interested in investigating if being above or below the median income (medloinc) impacts ACT means (act94) for schools. Complete the necessary steps to examine univariat
Conjugate prior : The distribution for samples from the particular probability distribution such that the posterior distribution at each stage of the sampling is of the identical f
Buffon's needle problem : A problem proposed and solved by the scientist Comte de Buffon in 1777 which includes determining the probability, p, which a needle of length l will inte
The Null Hypothesis - H0: β 1 = 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists The Alternative Hypothesis - H1: β 1 ≠ 0 i.e. there is no homoscedasti
Meta-analysis is the collection of techniques whereby the results of two or more independent studies are statistically combined to yield the overall answer to a question of intere
The estimator of the group by the time period interaction in a study in which the subjects in two different groups are observed in two different time periods. Normally one of th
Suppose that $4 million is available for investment in three projects. The probability distribution of the net present value earned from each project depends on how much is invest
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