On the robustness of least squares procedures in regression models

The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal distribution of errors in the context of univariate regression models, conditions on the design matrix are established under which the usual LRT of a linear hypothesis (under homoscedasticity of errors) remains valid if the errors have an intraclass covariance structure. The conditions hold in the case of some standard designs. The relevance of C. R. Rao's (1967 In Proceedings Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, pp. 355–372) and G. Zyskind's (1967, Ann. Math. Statist.38 1092–1110) conditions in this context is discussed.     

Local generalized empirical estimation of regression

Let f(x) be the density of a design variable X and m(x) = E[Y\X = x] the regression function. Then m(x) - G(x)/f(x), where G(x) = m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn (x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial of order p approximation to Gn(.) which provides estimators of the function G(x) and its derivatives. The density f(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the     

An empirical fit to estimated neutron emission cross sections from proton induced reactions

Neutron emission cross section for various elements from⁹Be to²⁰⁹Bi have been calculated using the hybrid model code ALICE-91 for proton induced reactions in the energy range 25 MeV to 105 Me V. An empirical expression relating neutron emission cross section to target mass number and incident proton energy has been obtained. The simple expression reduces the computation time significantly. The trend in the variation of neutron emission cross sections with respect to the target mass number and incident proton energy has been discussed within the framework of the model used.     

On a kind of integrals of empirical processes concerning insurance risk

This paper proves the strong consistence and the central limit theorems for empirical right tail deviations.     

On the efficiency of selection criteria in spline regression

This paper concerns the cubic smoothing spline approach to nonparametric regression. After first deriving sharp asymptotic formulas for the eigenvalues of the smoothing matrix, the paper uses these formulas to investigate the efficiency of different selection criteria for choosing the smoothing parameter. Special attention is paid to the generalized maximum likelihood (GML), C _p and extended exponential (EE) criteria and their marginal Bayesian interpretation. It is shown that (a) when the Bayesian model that motivates GML is true, using C _p to estimate the smoothing parameter would result in a loss of efficiency with a factor of 10/3, proving and strengthening a conjecture proposed in Stein (1990); (b) when the data indeed come from the C _p density, using GML would result in a loss of efficiency of ; (c) the loss of efficiency of the EE criterion is at most 1.543 when the data are sampled from its consistent density family. The paper not only studies equally spaced observations (the setting of Stein, 1990), but also investigates general sampling scheme of the design points, and shows that the efficiency results remain the same in both cases.This work is supported in part by NSF grant DMS-0204674 and Harvard University Clark-Cooke Fund. Mathematics Subject Classification (2000):Primary: 62G08; Secondary: 62G20     

A Large Sample Approximation to the Profile Plug-in Upper Confidence Limit

We consider the problem of constructing a 1– upper confidence limit for the scalar parameter ₀ in the presence of the nuisance parameter vector ₀, when the data are discrete. The 'profile plug-in' upper confidence limit is introduced by Kabaila and Lloyd. This confidence limit is based on computing a P-value from an estimator of ₀, replacing the nuisance parameter by the profile maximum likelihood estimate for known, and equating to . Theoretical and numerical evidence for the good coverage properties of this confidence limit is presented by Kabaila and Lloyd. An upper confidence limit should be assessed not only by its coverage properties but also by how large this confidence limit is. We measure how large the profile plug-in upper limit is by using a large sample approximation to it. This large sample approximation is used to delineate further the good properties of this confidence limit.     

Remarks on Estimation Problem for Stationary Processes in Continuous Time

The problem of estimating of the law (in the space of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure

Uniformly More Powerful, Two-Sided Tests for Hypotheses about Linear Inequalities

Let Xhave a multivariate, p-dimensional normal distribution (p 2) with unknown mean and known, nonsingular covariance . Consider testing H ₀ : b _i 0, for some i = 1,..., k, and b _i 0, for some i = 1,..., k, versus H ₁ : b _i < 0, for all i = 1,..., k, or b _i < 0, for all i = 1,..., k, where b ₁,..., b _k , k 2, are known vectors that define the hypotheses and suppose that for each i = 1,..., k there is an j {1,..., k} (j will depend on i) such that b _i b _j 0. For any 0 < < 1/2. We construct a test that has the same size as the likelihood ratio test (LRT) and is uniformly more powerful than the LRT. The proposed test is an intersection-union test. We apply the result to compare linear regression functions.     

Deposition of Ni<Subscript> 13</Subscript> and Cu<Subscript> 13</Subscript> clusters on Ni(111) and Cu(111) surfaces

The soft deposition of Ni₁₃ and Cu₁₃ clusters on Ni(111) and Cu(111) surfaces is studied by means of constant-energy molecular-dynamics simulations. The atomic interactions are described by the Embedded Atom Method. It is shown that the shape of the nickel clusters deposited on Cu(111) surfaces remains rather intact, while the copper clusters impacting on Ni(111) surfaces collapse forming double and triple layered products. Furthermore, it is found that for an impact energy of 0.5 eV/atom the structures of all investigated clusters show the lowest similarity to the original structures, except for the case of nickel clusters deposited on a Cu(111) surface. Finally, it is demonstrated that when cluster and substrate are of different materials, it is possible to control whether the deposition results in largely intact clusters on the substrate or in a spreading of the clusters. This separation into hard and soft clusters can be related to the relative cohesive energy of the crystalline materials.