Biostatistics Virtual Seminar - Dr. Ghosh on High-Dimensional Mean Vector Test for One-Sided Hypothesis
When & Where
April 18, 2023
12:00 PM - 1:00 PM
WebEx ( View in Google Map)
Contact
- Scott Dyson
- [email protected]
Event Description
Presenter:
Santu Ghosh, Ph.D.
Associate Professor, Division of Biostatistics & Data Science, Augusta University
Abstract
Statistical inference plays a critical role in many scientific studies, and one important inference is mean vector testing. In high-dimensional data (the number of features, p, is larger than the number of observations, n), many efficient statistical methods for performing two-sided mean vector tests have been developed. However, one-sided high-dimensional mean vector tests have received limited attention. However, when n < p, the sample covariance matrix is singular with rank n. Consequently, the inverse matrix of sample covariance, which has been used in the conventional constructions of the multiple comparison procedure is not well-defined. Therefore, efficient and robust test in the high-dimensional setting is still in high demand. The proposed test method is based on the intuition that if the true values of the components µ are positive but small, then the sum across the components of the sample mean vector could be influenced by a large number of negative components of the sample mean vector. Thus, a sum-of-component based test statistic across all the indices will not likely be extreme enough to arouse suspicion of the null. A sum-of-maximum component based test statistic will represent an accumulation of a large number of positive but small signals and will have more power than the sum-of-component based test statistic. A one-sided high-dimensional mean vector test, known as the generalized maximum-component-wise (GMC) test, is proposed. We study the asymptotic distribution of GMC test statistic. The proposed test achieves competitive rates for both type I error and power. The usefulness of the suggested test is illustrated by applications to the EpiGO study.
Password: VAqpMQpR624
Event Site Link
https://uthealth.webex.com/uthealth/j.php?MTID=m9e2df2ca0d53ec7cbb831331dc7161ca
Additional Information
Presenter:
Santu Ghosh, Ph.D.
Associate Professor, Division of Biostatistics & Data Science, Augusta University
Abstract
Statistical inference plays a critical role in many scientific studies, and one important inference is mean vector testing. In high-dimensional data (the number of features, p, is larger than the number of observations, n), many efficient statistical methods for performing two-sided mean vector tests have been developed. However, one-sided high-dimensional mean vector tests have received limited attention. However, when n < p, the sample covariance matrix is singular with rank n. Consequently, the inverse matrix of sample covariance, which has been used in the conventional constructions of the multiple comparison procedure is not well-defined. Therefore, efficient and robust test in the high-dimensional setting is still in high demand. The proposed test method is based on the intuition that if the true values of the components µ are positive but small, then the sum across the components of the sample mean vector could be influenced by a large number of negative components of the sample mean vector. Thus, a sum-of-component based test statistic across all the indices will not likely be extreme enough to arouse suspicion of the null. A sum-of-maximum component based test statistic will represent an accumulation of a large number of positive but small signals and will have more power than the sum-of-component based test statistic. A one-sided high-dimensional mean vector test, known as the generalized maximum-component-wise (GMC) test, is proposed. We study the asymptotic distribution of GMC test statistic. The proposed test achieves competitive rates for both type I error and power. The usefulness of the suggested test is illustrated by applications to the EpiGO study.
Password: VAqpMQpR624
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