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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 boot-strap methods for constructing confidence bands in the class of esti-mators that converge at rate cube-root n. The Grenander estimator (see Grenander (1956)), the nonparametric maximum likelihood esti-mator of an unknown non-increasing density function f on [0, ∞), is a prototypical… (More)

SUMMARY We introduce a method based on a pseudolikelihood ratio 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. One seeks to estimate the distribution of time… (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)

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] d , B), ; L 1) in terms of the relevant constants, where d ≥ 1, a < b ∈ R, B > 0, and C([a, b] d , B) denotes the set of all convex functions on [a, b] d that are… (More)

Let (X, Z) be a continuous random vector in R × R d , d ≥ 1. In this paper, we define the notion of a nonparametric residual of X on Z that is always independent of the predictor Z. We study its properties and show that the proposed notion of residual matches with the usual residual (error) in a multivariate normal regression model. Given a random vector… (More)

- Bodhisattva Sen
- 2005

The concept of Fractile Graphical Analysis (FGA) was introduced by Pras-anta Chandra Mahalanobis (see Mahalanobis, 1960). It is one of the earliest nonparametric regression techniques to compare two regression functions for two bivariate populations (X, Y). This method is particularly useful for comparing two regression functions where the covariate (X) for… (More)

We investigate the performance of model based bootstrap methods for constructing point-wise confidence intervals around the survival function with interval censored data. We show that bootstrapping from the nonparamet-ric maximum likelihood estimator of the survival function is inconsistent for both the current status and case 2 interval censoring models. A… (More)

In this paper we investigate the (in)-consistency of different boot-strap 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 non-increasing density function f on [0, ∞), is a prototypical example. We focus on this example… (More)

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