TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 73

SAS/Ets User's Guide 73. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 712 F Chapter 12 The ENTROPY Procedure Experimental proc reg data one outest parm3 model y x1 x2 by by run The 100 estimations of the coefficient on variable x1 are then summarized for each of the three error distributions by using PROC UNIVARIATE as follows proc univariate data parm1 var x1 run The following table summarizes the results from the estimations. The true value for the coefficient on x1 is . Estimation Method Normal Chi-Squared Mean Cauchy Std Deviation Mean Std Deviation Mean Std Deviation GME .330 GME-NM OLS For normally distributed or nearly normally distributed data moment-constrained maximum entropy is a good choice. For distributions not well described by a normal distribution data-constrained maximum entropy is a good choice. Example Unreplicated Factorial Experiments Factorial experiments are useful for studying the effects of various factors on a response. For the practitioner constrained to the use of OLS regression there must be replication to estimate all of the possible main and interaction effects in a factorial experiment. Using OLS regression to analyze unreplicated experimental data results in zero degrees of freedom for error in the ANOVA table since there are as many parameters as observations. This situation leaves the experimenter unable to compute confidence intervals or perform hypothesis testing on the parameter estimates. Several options are available when replication is impossible. The higher-order interactions can be assumed to have negligible effects and their degrees of freedom can be pooled to create the error degrees of freedom used to perform inference on the lower-order estimates. Or if a preliminary experiment is being run a normal probability plot of all effects can provide insight as to which effects are significant and therefore focused in a later more complete experiment. The following example illustrates the

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