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Statistics48

<MVUE>Complete sufficient statistics/ Rao-Blackwell Theorem/Lehmann Scheffe Theorem/Exponential family/Basu Theorem Complete Sufficient Statistics This will give you the information of another way to find Minimum variance unbiased estimator, which is the best estimator of parameters. As I mentioned in the previous post, MSE(Mean Squared Error) is a good indicator of the difference between estimator and the parameter. As Mean Squared value can be expressed as Var(T(X))-bias^2, you should find the minimum varia.. 2020. 9. 13.
Sufficient Statistics Sufficiency : T(X1, X2,..., Xn) is said to have 'sufficiency' for the parameter, if the conditional of X1, X2,...Xn given T=t does not rely on the value of the parameter. And the T(X1,X2,X3,...,Xn) is called 'Sufficient Statistics.' That is, by gaining T we need no longer to find knowledge about the parameter from random samples. Figuring out whether the conditional of X1, X2,...Xn given T=t doe.. 2020. 9. 10.
<MVUE>Cramer-Lao Lower bound/ Information Inequality /Fisher's Information/Information Inequality /Properties/Normal Approximation Let T(X) be the unbiased estimator of g(θ). Among available unbiased estimators what satisfy E(T(X))=g(θ), you can find the most favorable estimator with Mean Square Error. Mean square error, which is usually denoted as MSE is the expected value of squared error which is one of loss functions. The reason for computing the expected value of the loss function is that T(X) is the function of a rand.. 2020. 9. 3.
F distribution F - distribution F distribution is a distribution with two degrees of freedom which is usually notated as n(df1) and m(df2). The distribution is highly related to Chi-square distribution, also related to a gamma distribution, beta distribution ,and t distribution. F distribution table usually exists for a=0.1, 0.05, 0.025, 0.01, 0.001I will show two cases when a=0.1 and a=0.05 1. F table for a=0.. 2020. 8. 25.
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