We consider testing for homogeneity in a two-sample problem in which one of the samples has a mixture structure. The problem arises naturally in many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials. In this paper, we suggest using the modified likelihood ratio te...

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria tha...

2000 We extend the Semiparametric Likelihood Ratio Theorem of Murphy and Van del' Vaart for one-dimensional to Euclidean paramet(;rs of auy dimension. The as:VIrlptotic distribution of the likelihood ratio statistic for testing a k-dimensional Euclidean paramet'"r is shown to be the usual under the null hypothesis. This result is useful not only for testing purposes but also in forming likeliho...

Using nonconvex penalized least squares, we propose a class of variable selection procedures for linear models and partially linear models when the covariates are measured with additive error. The rate of convergence and the asymptotic normality of the resulting estimate are established. We further demonstrate that, with proper choice of penalty functions and the regularization parameter, the r...

We consider two variations on a Lehmann alternatives to symmetry-at-zero semiparametric model, with a real parameter θ quantifying skewness and a symmetric-at-0 distribution as a nuisance function. We show that a test of symmetry based on the signed logrank statistic (Hall [2011]) is asymptotically efficient in these models, derive its properties under local alternatives and present efficiency ...

Bartholomew and Leung proposed a limited-information goodness-of-fit test statistic (Y) for models fitted to sparse 2(P ) contingency tables. The null distribution of Y was approximated using a chi-squared distribution by matching moments. The moments were derived under the assumption that the model parameters were known in advance and it was conjectured that the approximation would also be app...

In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegration relationships. We propose a non-parametric test statistic for testing the null hypothesis of two independent random walks against wide cointegrating alternatives including monotonic nonlinearities and certain types of level shifts in the cointegration relationshi...

if we use the convention that additive terms that do not contain the parameter may be dropped from log likelihoods (because they do not affect any likelihood-based statistical inferences). Thus we have another definition of exponential families: a statistical model is an exponential family of distributions if there exists a statistic Y and a parameter θ such that the log likelihood has the form...

Linear algebra is used to demonstrate two important assertions in the main text: (1) that the expectation value of the chi-square statistic χ is equal to the degrees of freedom—the number of data points less the number of fit parameters and (2) the “∆χ = 1” rule—which states that if any fit parameter is offset one standard deviation from its best-fit value, the minimum χ (with that parameter fi...