Motivated by a representation for the least squares estimator, we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time. They are unbiased for homoscedastic errors and a special case, the delete-one jackknife, is almost unbiased for heteroscedastic errors. The method is extended to cover nonlinear parameters, regression $M$-estimators, nonlinear regression and generalized linear models. Interval estimators can be constructed from the jackknife histogram. Three bootstrap methods are considered. Two are shown to give biased variance estimators and one does not have the bias-robustness property enjoyed by the weighted delete-one jackknife. A general method for resampling residuals is proposed. It gives variance estimators that are bias-robust. Several bias-reducing estimators are proposed. Some simulation results are reported.

/pdf/jackknife-bootstrap-and-other-resampling-methods-in-3l6x5quxzs.pdf

Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis

In this paper, we provide a review of statistical methods that are useful in conducting computer experiments. Our focus is on the task of metamodeling, which is driven by the goal of optimizing a complex system via a deterministic simulation model. However, we also mention the case of a stochastic simulation, and examples of both cases are discussed. The organization of our review first presents several engineering applications, it then describes approaches for the two primary tasks of metamodeling: (i) selecting an experimental design; and (ii) fitting a statistical model. Seven statistical modeling methods are included. Both classical and newer experimental designs are discussed. Finally, our own computational study tests the various metamodeling options on two two-dimensional response surfaces and one ten-dimensional surface.

A review on design, modeling and applications of computer experiments

Bayes Factors for Linear and Log-Linear Models with Vague Prior Information

Supersaturated designs are very cost-effective to scientists and engineers at the primary stage of scientific investigation. This article describes a method of constructing supersaturated designs from balanced incomplete block designs that is a generalization of the method of Lin for constructing these designs and a more general approach to constructing these designs.

/pdf/an-algorithmic-approach-to-constructing-supersaturated-2xl2g91vru.pdf

An algorithmic approach to constructing supersaturated designs

Previous work on polyphase complementary codes is reviewed, and a number of new results are presented including additional kernels and lengths. Generating methods from other binary and polyphase sequences are given and negative results of other existence searches reported. Advantages of specialized forms for radar and Loran-C are discussed, including complementary Barker codes. A table of known lengths of pairs, triads and quads of sequences is given.

Polyphase complementary codes

An $n \times n$ matrix $H$ with all its entries $+1$ and $-1$ is Hadamard if $HH' = nI$. It is well known that $n$ must be 1, 2 or a multiple of 4 for such a matrix to exist, but is not known whether Hadamard matrices exist for every $n$ which is a multiple of 4. The smallest order for which a Hadamard matrix has not been constructed is (as of 1977) 268. Research in the area of Hadamard matrices and their applications has steadily and rapidly grown, especially during the last three decades. These matrices can be transformed to produce incomplete block designs, $t$-designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III designs, optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects. In this paper we survey the existence of Hadamard matrices and many of their applications.

https://projecteuclid.org/download/pdf_1/euclid.aos/1176344370

W. D. Wallis

Papers

Hadamard Matrices and Their Applications