Confidence Regions for Robust Regression

This paper describes the results of a Monte Carlo study of certain aspects of robust regression confidence region estimation for linear models with one, five, and seven parameters. One-step sine estimators (c = l.42) were used with design matrices consisting of short-tailed, Gaussian, and long-tailed columns. The samples were generated from a variety of contaminated Gaussian distributions. A number of proposals for covariance matrices were tried, including forms derived from asymptotic considerations and from weighted-least squares with data dependent weights. Comparisons with: the Monte Carlo "truth" were made using generalized eigenvalues. In order to measure efficiency and compute approximate t-values, linear combinations of parameters corresponding to the largest eigenvalues of the "truth" were examined. For design matrices with columns of modest kurtosis, the covariance estimators all give reasonable results and, after adjusting for asymptotic bias, some useful approximate t-values can be obtained. This implies that the standard weighted least-squares output using data-dependent weights need only be modified slightly to give useful robust confidence intervals. When design matrix kurtosis is high and severe contamination is present in the data, these simple approximations are not adequate.

Linear Regression Diagnostics

This paper attempts to provide the user of linear multiple regression with a battery of diagnostic tools to determine which, if any, data points have high leverage or influence on the estimation process and how these possibly discrepant data points differ from the patterns set by the majority of the data. The point of view taken is that when diagnostics indicate the presence of anomolous data, the choice is open as to whether these data are in fact unusual and helpful, or possibly harmful and thus in need of modifications or deletion. The methodology developed depends on differences, derivatives, and decompositions of basic regression statistics. There is also a discussion of how these techniques can be used with robust and ridge estimators. An example is given showing the use of diagnostic methods in the estimation of a cross-country savings rate model.

The Variances of Regression Coefficient Estimates Using Aggregate Data

This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.

Robust Non-Linear Regression Using The Dogleg Algorithm

What are the statistical and computational problems associated with robust nonlinear regression? This paper presents a number of possible approaches to these problems and develops a particular algorithm based on the work of Powell and Dennis.

Teaching Simulations Supported by Artificial Intelligence in the Real World

Video conferencing has enabled synchronous communication in a classroom and created multi-sensory content to stimulate learners. Artificial intelligence involves complex equations that are better taught using a constructive pedagogy where students experiment with alternative ways of solving the same problem. Multiple-choice questions have high reliability and can easily reveal student skill levels in a quick way. The Australian Computer Society accreditation exercise ensures that the content for each subject serves as a flexible template for teaching. The geographical extent of the country requires the presence of multiple subordinate campuses affiliated to a main campus. Following the concept of strands, it was also necessary to show continuity in learning and assessments between the first- and second-year subjects. Student feedback for subjects with artificial intelligence-based simulations showed that several students found it difficult to understand lectures and assignments. Hence, to measure student learning, we introduced a Kahoot quiz during the recess of each lecture that students could join through their mobile phones from different campuses. Software project management is challenging for students with vision or attention-related disorders. We taught them how to use charts to visually observe variables and narrow down possible relationships before performing in-depth analysis. One of the main purposes of education is employability. Hence, greater context to real world industry examples was introduced into lectures

Graphics for Data Analysis

In recent years, graphics have become an essential part of modern data analysis. This paper describes a system called CLOUDS which is designed to make available on inexpensive storage tube terminals a wide range of graphic tools related to data analysis, economics, and management science. The system can be accessed nationwide by nonprofit organizations via the National Bureau of Economic Research computer network.

Multi-strata subsurface laser die singulation to enable defect-free ultra-thin stacked memory dies

We report the extension of multi-strata subsurface infrared (1.342 μm) pulsed laser die singulation to the fabrication of defect-free ultra-thin stacked memory dies. We exploit the multi-strata interactions between generated thermal shockwaves and the preceding high dislocation density layers formed to initiate crack fractures that separate the individual dies from within the interior of the die. We show that optimized inter-strata distances between the high dislocation density layers together with effective laser energy dose can be used to compensate for the high backside reflectance (up to ∼ 82%) wafers. This work has successfully demonstrated defect-free eight die stacks of 25 μm thick mechanically functional and 46 μm thick electrically functional memory dies.Sandisk SemiConductor Shanghai Co Ltd.Leaders for Global Operations ProgramNoyce Foundation (Robert N. Noyce full scholarship