- Question 12 A Researcher Plans To Use A Random Sample X1 Xin Of Size N From A Population With Probability Density 1 (141.19 KiB) Viewed 27 times
)Question 12 A researcher plans to use a random sample X1, ..., Xin of size n from a population with probability density function ) x > 0 = f(zlo) = { $07/20 elsewhere, where parameter 0 > 0. (a) Derive the maximum likelihood estimator for parameter - (b) Derive an expression for the test statistic LRS = –2 In A for undertaking a likeli- hood ratio test of the null hypothesis H. : 0 = 1 against the alternative hypothesis H1 : 0 + 1. = : (c) The researcher is concerned that the application is for a small sample size, n, and does not wish to rely on asymptotic results concerning the distribution of LRS. Explain how you would use simulation methods to determine the small sample distribution of the test statistic LRS and how it could be used to undertake the above hypothesis test in small samples.