Mar 2. (34%) Suppose we wish to estimate the center (location) of a symmetric distribution. Four possible estimators are

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Mar 2 34 Suppose We Wish To Estimate The Center Location Of A Symmetric Distribution Four Possible Estimators Are 1 (59.05 KiB) Viewed 25 times

Mar 2. (34%) Suppose we wish to estimate the center (location) of a symmetric distribution. Four possible estimators are: (1) the sample mean, 2, (m) the sample median, m, (ii) the midrange and (iv) the midquartile (939). To compare the properties cach of these estimators with respect to unbiasedness and variability, you will conduct a simulation study. To do so you will: a) Generate random samples of size n from the specified distributions (below) b) For each sample, compute the four estimators c) Repeat M times. From the output from each simulation, obtain descriptive statistics for the M = 1000 values of each estimator that must include the mean and standard deviation of the estimates). For each of the sample sizes, construct () density estimates of the four estimators on the same plot, (m) comparative boxplots, and (iii) pairs plots of the four estimators Distributions: N(0, 1), Unif(0, 1), Exp(l) Sample Sizes: n = 10.30. 100 You need to perform 9 simulations To accomplish this you MUST write functions (or use replicate) (one for each distribution) that will perform the simulations and retum a data frame containing the M sets of estimates of the four estimators. The post simulation calculations and construction of graphs need not be a part of the function. a You must summarize the results of the simulation study by creating nice" summary tables in Word - see below) and write a paragraph (or few) referring to the output, graphs, and tables as necessary. The table must include the value of the parameter you are trying to estimate. The actual code and output must be in the electronic appendices What happens to the distributions of the estimators as n increases? Consider: unbiasedness (the mean of the estimates being close to the correct" value). • the variability of the estimator, and • how the shape of the distribution of the estimator behaves as n gets larger. For each underlying distribution, which statistic would you choose to estimate the center location"? Give reasons. Meanu Hints Distribution NO.1) Unifo, 1) Medias 0 Sid. Devo 1 0 QI -0.674 0.25 Q3 0.674 0.75 0.5 0.5 -0.2887 Exp(1.) 1 -1805) -0.6931 1 0.288 1.386 You will need to make three such tables - one each for the normal, uniform, and exponential distributions F Me Sul de Meas Medan M