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Estimating the integral of a squared regression function with Latin hypercube sampling

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  • Loh, Wei-Liem

Abstract

This article is concerned with the estimation of the integral of a squared regression function using Latin hypercube sampling. A class of generalized nearest-neighbour estimators is proposed and their properties are investigated with respect to various smoothness classes of regression functions. In particular, mild conditions are established which ensure that achieves a root-n convergence rate. It is further shown that has an asymptotic mean squared error smaller than that of any regular estimator based on an i.i.d. sample of the same size.

Suggested Citation

  • Loh, Wei-Liem, 1997. "Estimating the integral of a squared regression function with Latin hypercube sampling," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 339-349, February.
    • Handle: RePEc:eee:stapro:v:31:y:1997:i:4:p:339-349
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    References listed on IDEAS

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    1. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
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