Bodhisattva Sen

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In this paper, we study the covering numbers of the space of convex and uniformly bounded functions in multidimension. We find optimal upper and lower bounds for the <formula formulatype="inline"> <tex Notation="TeX">$\epsilon $</tex></formula>-covering number of <formula formulatype="inline"><tex Notation="TeX">$ {\cal C}([a, b]^{d}, B)$</tex></formula>,(More)
In this paper we investigate the (in)-consistency of different bootstrap methods for constructing confidence bands in the class of estimators that converge at rate cube-root n. The Grenander estimator (see Grenander (1956)), the nonparametric maximum likelihood estimator of an unknown non-increasing density function f on [0,∞), is a prototypical example. We(More)
This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a "sensitive time point", is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The(More)
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the -covering number M(C([a, b], B), ;L1) in terms of the relevant constants, where d ≥ 1, a < b ∈ R, B > 0, and C([a, b], B) denotes the set of all convex functions on [a, b] that are uniformly(More)
In this paper we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate n 1 3 . The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0,∞), is a prototypical example. We focus on this example(More)
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation(More)
In this paper we consider the problem of constructing confidence intervals in the presence of nuisance parameters. We discuss a generalization of the unified method of Feldman and Cousins (1998) with nuisance parameters. We demonstrate our method with several examples that arise frequently in High Energy Physics and Astronomy. We also discuss the hybrid(More)
We introduce a pseudo-likelihood ratio based method for estimating the distribution function of the survival time in a mixed case interval censoring model. In a mixed case model, an individual is observed a random number of times, and at each time it is recorded whether an event has happened or not. Based on this data, one seeks to estimate the distribution(More)