Plenary Lecture

Confidence Intervals and t-Percentiles: Improved Diagnostics under Two-stage Sampling Strategies

Professor Nitis Mukhopadhyay
Department of Statistics
University of Connecticut-Storrs

Connecticut, USA.


Abstract: Student’s t percentiles (t_(ν,α)) are indispensable in the construction of confidence intervals and tests for the mean of a normal distribution when population variance is unknown. One customarily feels at ease to replace t_(ν,α) with the percentile z_α from a standard normal distributionwhen v is “large” (v≥30: frequently used as a guide). In this day and age, however, one often handles large sets of data and hence it has become rather simple to reasonably justify that v is large indeed. While this thought-process sounds practical, useful, and reasonable, it is clearly the case that z_α does not involve the sample size at all whereas t_(ν,α) does.

In this presentation, we will highlight a new diagnostic descriptor of t_(ν,α) which (i) involves v, α and z_α but not t_(ν,α), (ii) is easily accessible, and (iii) is more informative than z_α in the sense that the new descriptor lies strictly between t_(ν,α) and z_αwhatever be v, large or small. These will be amply appended by brief data analysis.

Brief Biography of the Speaker: Prof. Nitis Mukhopadhyay received PhD degree (1975) from the Indian Statistical Institute-Calcutta. He has been a full professor in the Department of Statistics, University of Connecticut-Storrs, USA since 1985. He served as the Head of this department during 1987-1990.

Prior to joining the University of Connecticut, Prof. Mukhopadhyay was a faculty member at the following institutions: Monash University-Melbourne, Australia (1976-77), University of Minnesota-Minneapolis (1977-78), University of Missouri-Columbia (1978-79), and Oklahoma State University-Stillwater (1979-85).

He made prolific contributions in a number of areas including statistical inference-parametric and nonparametric, sequential analysis, multiple comparisons, clinical trials, applied probability, econometrics, and broad ranging applications. Prof. Mukhopadhyay is especially recognized for path-breaking contributions in (i) sequential analysis as well as (ii) selection and ranking. His honors include elected Fellows of the Institute of Mathematical Statistics (2002), the American Statistical Association (2003), the American Association for the Advancement of Science (2012), elected Member of the International Statistical Institute (2007), elected Member of Connecticut Academy of Arts and Sciences (2014), Fellow of the Royal Statistical Society, the Abraham Wald Prize in Sequential Analysis (2008), and the Don Owen Award (2015).

The Honorary Fellowship from the Institute of Applied Statistics Sri Lanka was bestowed upon him in 2017. He has been the Editor-in-Chief for the premier journal, Sequential Analysis, since 2004 and serves as an Associate Editor for a number of leading international journals.

Prof. Mukhopadhyay has (co)authored 6 books, 18 book chapters, nearly 300 peer-reviewed research papers, and edited or co-edited more than 7 special volumes. He has supervised 26 Ph.D. students as a major adviser and has 4 Ph.D. continuing under his guidance at this time. His former PhD advisees have successful careers in academia, businesses, and industries and they have made their own marks.
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