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In modern statistical applications, the dimension of covariates can be much larger than the sample size, and extensive research has been done on screening methods which can effectively reduce the dimensionality. However, the existing feature screening procedure can not be used to handle the ultrahigh-dimensional survival data problems when failure indicators are missing at random. This motivates us to develop a feature screening procedure to handle this case. In this paper, we propose a feature screening procedure by sieved nonparametric maximum likelihood technique for ultrahigh-dimensional survival data with failure indicators missing at random. The proposed method has several desirable advantages. First, it does not rely on any model assumption and works well for nonlinear survival regression models. Second, it can be used to handle the incomplete survival data with failure indicators missing at random. Third, the proposed method is invariant under the monotone transformation of the response and satisfies the sure screening property. Simulation studies are conducted to examine the performance of our approach, and a real data example is also presented for illustration. [ABSTRACT FROM AUTHOR]

This paper proposes a test for assessing the accuracy of an assumed nonlinear regression model with long memory design and heteroscedastic long memory errors. The test is based on the marked empirical process. The asymptotic distributions of the proposed test statistics are investigated. The leave-one-observation-out kernel type estimator of the conditional variance function is also constructed in order to implement the lack of fit test. [ABSTRACT FROM AUTHOR]

Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation under non-normal error distribution. However, at least in principle, quantile regression (QR) is more robust in the presence of outliers/influential observations and misspecification of the error distributions when compared to the conventional mean regression approach. In this context, this paper develops a likelihood-based approach for estimating QR models with correlated continuous longitudinal data using the asymmetric Laplace distribution. Our approach relies on the stochastic approximation of the EM algorithm (SAEM algorithm), obtaining maximum likelihood estimates of the fixed effects and variance components in the case of nonlinear mixed effects (NLME) models. We evaluate the finite sample performance of the SAEM algorithm and asymptotic properties of the ML estimates through simulation experiments. Moreover, two real life datasets are used to illustrate our proposed method using the qrNLMM package from R . [ABSTRACT FROM AUTHOR]

In this paper we address the issue of testing inference of the dispersion parameter in heteroscedastic symmetric nonlinear regression models considering small samples. We derive Bartlett corrections to improve the likelihood ratio as well modified profile likelihood ratio tests. Our results extend some of those obtained in Cordeiro (J Stat Comput Simul 74:609–620, 2004) and Ferrari et al. (J Stat Plan Inference 124:423–437, 2004), who consider a symmetric nonlinear regression model and normal linear regression model, respectively. We also present the bootstrap and bootstrap Bartlett corrected likelihood ratio tests. Monte Carlo simulations are carried out to compare the finite sample performances of the three corrected tests and their uncorrected versions. The numerical evidence shows that the corrected modified profile likelihood ratio test, the bootstrap and bootstrap Bartlett corrected likelihood ratio test perform better than the other ones. We also present an empirical application. [ABSTRACT FROM AUTHOR]

We investigate properties of optimal designs under the second-order least squares estimator (SLSE) for linear and nonlinear regression models. First we derive equivalence theorems for optimal designs under the SLSE. We then obtain the number of support points in A-, c- and D-optimal designs analytically for several models. Using a generalized scale invariance concept we also study the scale invariance property of D-optimal designs. In addition, numerical algorithms are discussed for finding optimal designs. The results are quite general and can be applied for various linear and nonlinear models. Several applications are presented, including results for fractional polynomial, spline regression and trigonometric regression models. [ABSTRACT FROM AUTHOR]

We introduce a powerful and yet seldom used numerical approach in statistics for solving a broad class of optimization problems where the search space is discretized. This optimization tool is widely used in engineering for solving semidefinite programming (SDP) problems and is called self-dual minimization (SeDuMi). We focus on optimal design problems and demonstrate how to formulate A-, A s -, c-, I-, and L-optimal design problems as SDP problems and show how they can be effectively solved by SeDuMi in MATLAB. We also show the numerical approach is flexible by applying it to further find optimal designs based on the weighted least squares estimator or when there are constraints on the weight distribution of the sought optimal design. For approximate designs, the optimality of the SDP-generated designs can be verified using the Kiefer–Wolfowitz equivalence theorem. SDP also finds optimal designs for nonlinear regression models commonly used in social and biomedical research. Several examples are presented for linear and nonlinear models. [ABSTRACT FROM AUTHOR]

Under a nonlinear regression model with univariate response an algorithm for the generation of sequential adaptive designs is studied. At each stage, the current design is augmented by adding p design points where p is the dimension of the parameter of the model. The augmenting p points are such that, at the current parameter estimate, they constitute the locally D-optimal design within the set of all saturated designs. Two relevant subclasses of nonlinear regression models are focused on, which were considered in previous work of the authors on the adaptive Wynn algorithm: firstly, regression models satisfying the 'saturated identifiability condition' and, secondly, generalized linear models. Adaptive least squares estimators and adaptive maximum likelihood estimators in the algorithm are shown to be strongly consistent and asymptotically normal, under appropriate assumptions. For both model classes, if a condition of 'saturated D-optimality' is satisfied, the almost sure asymptotic D-optimality of the generated design sequence is implied by the strong consistency of the adaptive estimators employed by the algorithm. The condition states that there is a saturated design which is locally D-optimal at the true parameter point (in the class of all designs). [ABSTRACT FROM AUTHOR]