Algebraic Geometry  and Commutative Algebra seminar

Tuesday, 05 February 2023, 11:30 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR Mumbai (retd)

Title: Local Criterion for Flatness

Statistics Seminar

Tuesday, 7th February, 3:30 pm

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Venue: Ramanujan Hall

Host: Sanjeev Sabnis

Speaker: Sujit Ghosh

Affiliation: North Carolina State University

Title: Possible Hazards of Some Popular Hazard Rate Models

Abstract: The Cox proportional hazard (PH) model is widely used to determine the effects of risk factors and treatments on survival time of subjects that might be right censored. The selection of covariates depends crucially on the specific form of the conditional hazard model, which is often assumed to be PH, accelerated failure time (AFT), or proportional odds (PO). However, it is shown that none of these semiparametric models allow for the crossing of the survival functions and hence such assumptions, although popular, may adversely affect the selection of risk factors. Moreover, the most commonly used PH assumption may also be violated when there is a delayed effect of the risk factors. A sequence of Bernstein polynomials based model is instead presented which provides (i) a smooth estimator of the conditional hazard and can be shown to be a unique solution of a strictly convex optimization problem; making it computationally attractive, (ii) a model that encompasses PH structure, and (iii) large sample properties including consistency and convergence rates can be established under a set of mild regularity conditions. Empirical results based on several simulated data scenarios indicate the superior performances of the model, and thereby shown to avoid possible hazards of some of the commonly used hazard rate models. The presentation is based on some ongoing work and the following published articles: (i) Osman and Ghosh (2012) and (ii) Sheng and Ghosh (2019).

Algebraic Groups Seminar

Tuesday, 7 February 2023, 4 pm

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Venue: Room 215

Host:Shripad M. Garge

Speaker: Deepkumar Makadiya

Affiliation: IIT Bombay

Title: Linear algebraic groups, basic themes. II

Abstract: This lecture will be devoted to proving that every affine algebraic group is linear.