Arup Bose

Generalized bootstrap for estimating equations

We introduce a generalized bootstrap technique for estimators obtained by solving estimating equations. Some special cases of this generalized bootstrap are the classical bootstrap of Efron, the delete-d jackknife and variations of the Bayesian bootstrap. The use of the proposed technique is discussed in some examples. Distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained.

Limiting spectral distribution of a special circulant

The limiting spectral distribution of random matrices is known only in a few special situations. In this article, we derive the limiting spectral distribution of a particular variant of a circulant random matrix. Our simulations demonstrate that the convergence to the limit is quite fast. Our method of proof also allows us to show that the limiting spectral distribution for a symmetric version of the Toeplitz matrix is the normal distribution.

ESTIMATING THE ARCH PARAMETERS BY SOLVING LINEAR EQUATIONS

This paper discusses the asymptotics of two-stage least squares estimator of the parameters of ARCH models. The estimator is easy to obtain since it involves solving two sets of linear equations. At the same time, the estimator has the same asymptotic efficiency as that of the widely used quasi-maximum likelihood estimator. Simulation results show that, even for small sample size, the performance of our estimator compared to the quasi-maximum likelihood estimator is better. Copyright 2003 Blackwell Publishing Ltd.

On the Performance of Linear Contracts

We examine the ability of linear contracts to replicate the performance of optimal unrestricted contracts in the canonical moral hazard setting with a wealth constrained, risk averse agent. We find that in a broad class of environments, the principal can always secure with a linear contract at least 95% of the profit that she secures with an optimal unrestricted contract, provided the productivity of the agents effort is not too meager.

Bootstrap in moving average models

We prove that the bootstrap principle works very well in moving average models, when the parameters satisfy the invertibility condition, by showing that the bootstrap approximation of the distribution of the parameter estimates is accurate to the ordero(n−1/2) a.s. Some simulation studies are also reported.

Equal Pay for Unequal Work: Limiting Sabotage in Teams

We demonstrate the value of “equal pay” policies in teams, even when team members have distinct abilities and make different contributions to team performance. A commitment to compensate all team members in identical fashion eliminates the incentive that each team member otherwise has to sabotage the activities of teammates in order to induce the team owner to implement a more favorable reward structure. The reduced sabotage benefits the team owner, and can secure Pareto gains under plausible circumstances.

Generalized bootstrap for estimators of minimizers of convex functions

We introduce a generalized bootstrap technique for estimators obtained by minimizing functions that are convex in the parameter. We establish the consistency of these schemes via representation theorems. A number of classical resampling schemes, like the delete-d jackknife may be treated as special cases of this generalized bootstrap; and new ways of resampling are also introduced. Some of the schemes are computationally more efficient than classical techniques.

Bootstrap confidence intervals

Nonparametric confidence bounds are obtained for a wide class of statistics using bootstrap. These results improve the errors in the probability estimates of the confidence intervals over the ones obtained by the normal approximation theory unconditionally.

Patterned Random Matrices and Method of Moments

We present a unified approach to limiting spectral distribution (LSD) of patterned matrices via the moment method. We demonstrate relatively short proofs for the LSD of common matrices and provide insight into the nature of different LSD and their interrelations. The method is flexible enough to be applicable to matrices with appropriate dependent entries, banded matrices, and matrices of the form Ap = 1 XX 0 where X is a p × n matrix with real entries and p ! 1 with n = n(p) ! 1 and p/n ! y with 0 � y < 1. This approach raises interesting questions about the class of patterns for which LSD exists and the nature of the possible limits. In many cases the LSD are not known in any explicit forms and so deriving probabilistic properties of the limit are also interesting issues.

Generalised bootstrap in non-regular M-estimation problems

For estimators of parameters defined as minimisers of Q([theta])=Ef([theta],X), we study the asymptotic and generalised bootstrap properties. We concentrate on the case where Q does not have adequate smoothness for standard analysis to work. We describe the properties required by Q as well as bootstrap weights for consistency of the bootstrap.