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On the Effect and Remedies of Shrinkage on Classification Probability Estimation

Pengarang : Chong Zhang
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 3)
Halaman : 134-142
Abstrak : Shrinkage methods have been shown to be effective for classification problems. As a form of regularization, shrinkage through penalization helps to avoid overfitting and produces accurate classifiers for prediction, especially when the dimension is relatively high. Despite the benefit of shrinkage on classification accuracy of resulting classifiers, in this article, we demonstrate that shrinkage creates biases on classification probability estimation. In many cases, this bias can be large and consequently yield poor class probability estimation when the sample size is small or moderate. We offer some theoretical insights into the effect of shrinkage and provide remedies for better class probability estimation. Using penalized logistic regression and proximal support vector machines as examples, we demonstrate that our proposed refit method gives similar classification accuracy and remarkable improvements on probability estimation on several simulated and real data examples.

Revisiting Immer’s Barley Data

Pengarang : -
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 3)
Halaman : 129-133
Abstrak : This article reexamines the famous barley data that are often used to demonstrate dot plots. Additional sources of supplemental data provide context for interpretation of the original data. Graphical and mixed-model analyses shed new light on the variability in the data and challenge previously held beliefs about the accuracy of the data. Supplementary materials for this article are available online.

Closed Likelihood Ratio Testing Procedures to Assess Similarity of Covariance Matrices

Pengarang : -
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 3)
Halaman : 117-128
Abstrak : In this article, we introduce a multiple testing procedure to assess a common covariance structure between k groups. The new test allows for a choice among eight different patterns arising from the three-term eigen decomposition of the group covariances. It is based on the closed testing principle and adopts local likelihood ratio (LR) tests. The approach reveals richer information about the underlying data structure than classical methods, the most common one being only based on homo/heteroscedasticity. At the same time, it provides a more parsimonious parameterization, whenever the constrained model is suitable to describe the real data. The new inferential methodology is then applied to some well-known datasets chosen from the multivariate literature. Finally, simulation results are presented to investigate its performance in different situations representing gradual departures from homoscedasticity and to evaluate the reliability of using the asymptotic χ2 to approximate the actual distribution of the local LR test statistics.

A federal perspective on prevention and behavioral health disparities in the Asian American and Pacific Islander population

Pengarang : Bui, Juliet; Dutta, Trina.
Nama Majalah/Jurnal : Asian American Journal of Psychology
Volume / Edisi : 5 (No. 2)
Halaman : 153-159
Abstrak : This special issue covers many programs and practices that align with federal efforts, as well as identifies challenges and opportunities for the federal government to better address the behavioral health needs of Asian Americans and Pacific Islanders (AAPIs). The studies in this issue in particular put a much needed focus on prevention within the AAPI community and discuss implications for research, practice, and policy. The timing of these studies and this special issue is especially important, given recent federal focus on prevention and behavioral health disparities. The Affordable Care Act (ACA; Patient Protection and Affordable Care Act, 2010) has increased attention on the role of prevention and spawned the National Prevention Strategy (National Prevention Council, 2011). Similarly, the ACA (2010) has heightened a focus on health disparities, leading to the creation of federal offices of minority health, a policy for more granular data collection of within-group subpopulations, and, most importantly, the first-ever U.S. Department of Health and Human Services (2011; HHS) HHS Action Plan to Reduce Racial and Ethnic Health Disparities. Driven by the ACA (2010) and the HHS Action Plan, the Substance Abuse and Mental Health Services Administration (SAMHSA) has elevated attention to behavioral health disparities and maintained a strategic focus on prevention. The studies in this special issue align remarkably well with these federal efforts.

The Power to See: A New Graphical Test of Normality

Pengarang : -
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 4)
Halaman : 249-260
Abstrak : Many statistical procedures assume that the underlying data-generating process involves Gaussian errors. Among the popular tests for normality, only the Kolmogorov–Smirnov test has a graphical representation. Alternative tests, such as the Shapiro–Wilk test, offer little insight as to how the observed data deviate from normality. In this article, we discuss a simple new graphical procedure which provides simultaneous confidence bands for a normal quantile–quantile plot. These bands define a test of normality and are narrower in the tails than those related to the Kolmogorov–Smirnov test. Correspondingly, the new procedure has greater power to detect deviations from normality in the tails. Supplementary materials for this article are available online.

The Mean Value Theorem and Taylor’s Expansion in Statistics

Pengarang : Changyong Feng
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 4)
Halaman : 245-248
Abstrak : The mean value theorem and Taylor’s expansion are powerful tools in statistics that are used to derive estimators from nonlinear estimating equations and to study the asymptotic properties of the resulting estimators. However, the mean value theorem for a vector-valued differentiable function does not exist. Our survey shows that this nonexistent theorem has been used for a long time in statistical literature to derive the asymptotic properties of estimators and is still being used. We review several frequently cited papers and monographs that have misused this “theorem” and discuss the flaws in these applications. We also offer methods to fix such errors.

Should the Interquartile Range Divided by the Standard Deviation be Used to Assess Normality?

Pengarang : Richard L. Warr
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 4)
Halaman : 242-244
Abstrak : We discourage the use of a diagnostic for normality: the interquartile range divided by the standard deviation. This statistic has been suggested in several introductory statistics books as a method to assess normality. Through simulation, we explore the rate at which this statistic converges to its asymptotic normal distribution, and the actual size of tests based on the asymptotic distribution at several sample sizes. We show that there are nonnormal distributions from which this method cannot detect a difference. Additionally, we show the power of this test for normality is quite poor when compared with the Shapiro–Wilk test.

Data Acquisition and Preprocessing in Studies on Humans: What is Not Taught in Statistics Classes?

Pengarang : -
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 4)
Halaman : 235-241
Abstrak : The aim of this article is to address issues in research that may be missing from statistics classes and important for (bio-) statistics students. In the context of a case study, we discuss data acquisition and preprocessing steps that fill the gap between research questions posed by subject matter scientists and statistical methodology for formal inference. Issues include participant recruitment, data collection training and standardization, variable coding, data review and verification, data cleaning and editing, and documentation. Despite the critical importance of these details in research, most of these issues are rarely discussed in an applied statistics program. One reason for the lack of more formal training is the difficulty in addressing the many challenges that can possibly arise in the course of a study in a systematic way. This article can help to bridge the gap between research questions and formal statistical inference by using an illustrative case study for a discussion. We hope that reading and discussing this article and practicing data preprocessing exercises will sensitize statistics students to these important issues and achieve optimal conduct, quality control, analysis, and interpretation of a study.

Intro Stats Students Need Both Confidence and Tolerance (Intervals)

Pengarang : -
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 4)
Halaman : 229-234
Abstrak : Tolerance intervals are typically not taught in introductory statistics courses aimed at business, engineering, and science majors. This is regrettable, since students are likely to encounter practical problems that should be analyzed using tolerance intervals. Additionally, contrasting tolerance intervals against confidence intervals will improve students’ understanding of confidence intervals, eliminating frequent confusions. In this article, we make the argument for teaching tolerance intervals in introductory statistics courses, and we offer suggestions about what to teach.

I Hear, I Forget. I Do, I Understand: A Modified Moore-Method Mathematical Statistics Course

Pengarang : -
Nama Majalah/Jurnal : The American Statistician
Volume / Edisi : 67 (No. 4)
Halaman : 219-228
Abstrak : Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs. Cohen described an adaptation with less explicit competition suitable for undergraduate students at a liberal arts college. This article details an adaptation of this modified Moore method to teach mathematical statistics, and describes ways that such an approach helps engage students and foster the teaching of statistics. Groups of students worked a set of three difficult problems (some theoretical, some applied) every two weeks. Class time was devoted to coaching sessions with the instructor, group meeting time, and class presentations. R was used to estimate solutions empirically, where analytic results were intractable, as well as to provide an environment to undertake simulation studies with the aim of deepening understanding and complementing analytic solutions. Each group presented comprehensive solutions to complement oral presentations. Development of parallel techniques for empirical and analytic problem solving was an explicit goal of the course, which also attempted to communicate ways that statistics can be used to tackle interesting problems. The group problem-solving component and use of technology allowed students to attempt much more challenging questions than they could otherwise solve. Supplementary materials for this article are available online.
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