The technology for building knowledge-based systems by inductive inference from examples has been demonstrated successfully in several practical applications. This paper summarizes an approach to synthesizing decision trees that has been used in a variety of systems, and it describes one such system, ID3, in detail. Results from recent studies show ways in which the methodology can be modified to deal with information that is noisy and/or incomplete. A reported shortcoming of the basic algorithm is discussed and two means of overcoming it are compared. The paper concludes with illustrations of current research directions.

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Induction of Decision Trees

Using research designs patterned after randomized experiments, many recent economic studies examine outcome measures for treatment groups and comparison groups that are not randomly assigned. By using variation in explanatory variables generated by changes in state laws, government draft mechanisms, or other means, these studies obtain variation that is readily examined and is plausibly exogenous. This paper describes the advantages of these studies and suggests how they can be improved. It also provides aids in judging the validity of inferences they draw. Design complications such as multiple treatment and comparison groups and multiple pre- or post-intervention observations are advocated.

Comparing Predictive Accuracy

Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial. In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n ≤ 15). For moderately sized samples (15 70), the formula range/6 gives the best estimator for the standard deviation (variance). We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy. Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported.

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Estimating the mean and variance from the median, range, and the size of a sample.

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite-sample tests are proposed, evaluated, and illustrated.

/pdf/comparing-predictive-accuracy-2tm17nazab.pdf

In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum and maximum values, and/or the first and third quartiles. Hence, in order to combine results, one may have to estimate the sample mean and standard deviation for such trials. In this paper, we propose to improve the existing literature in several directions. First, we show that the sample standard deviation estimation in Hozo et al.’s method (BMC Med Res Methodol 5:13, 2005) has some serious limitations and is always less satisfactory in practice. Inspired by this, we propose a new estimation method by incorporating the sample size. Second, we systematically study the sample mean and standard deviation estimation problem under several other interesting settings where the interquartile range is also available for the trials. We demonstrate the performance of the proposed methods through simulation studies for the three frequently encountered scenarios, respectively. For the first two scenarios, our method greatly improves existing methods and provides a nearly unbiased estimate of the true sample standard deviation for normal data and a slightly biased estimate for skewed data. For the third scenario, our method still performs very well for both normal data and skewed data. Furthermore, we compare the estimators of the sample mean and standard deviation under all three scenarios and present some suggestions on which scenario is preferred in real-world applications. In this paper, we discuss different approximation methods in the estimation of the sample mean and standard deviation and propose some new estimation methods to improve the existing literature. We conclude our work with a summary table (an Excel spread sheet including all formulas) that serves as a comprehensive guidance for performing meta-analysis in different situations.

/pdf/estimating-the-sample-mean-and-standard-deviation-from-the-21qt03q3yr.pdf

Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range

1. Probability and Distributions. 2. Multivariate Distributions. 3. Some Special Distributions. 4. Some Elementary Statistical Inferences 5. Consistency and Limiting Distributions 6. Maximum Likelihood Methods. 7. Sufficiency. 8. Optimal Tests of Hypotheses. 9. Inferences about Normal Models. 10. Nonparametric and Robust Statistics. 11. Bayesian Statistics. Appendix A. Mathematical Comments Appendix B. R-Functions. Appendix C. Tables of Distributions Appendix D. List of Common Distributions Appendix E. References Appendix F. Answers to Selected Exercises Index

http://www.gbv.de/dms/tib-ub-hannover/667409947.pdf

Introduction to Mathematical Statistics

Introduction to Mathematical Statistics (4th ed.).

Introduction to Mathematical Statistics.

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Introduction to Mathematical Statistics (6th Edition)

https://projecteuclid.org/download/pdf_1/euclid.aoms/1177731461

Allen T. Craig

Papers

Introduction to Mathematical Statistics

Introduction to Mathematical Statistics (4th ed.).

Introduction to Mathematical Statistics.

Introduction to Mathematical Statistics (6th Edition)

Note on the Independence of Certain Quadratic Forms