In this paper, we introduce a measurement error selection likelihood to select important variables and estimate additive components simultaneously in a high-dimensional additive model. Although the model contains multi-variates, the proposed estimation is a type of univariate nonparametric form. This format matches the feature of the additive structure in the sense that both the model and the nonparametric estimation are of univariate nonparametric feature, essentially. Consequently, the variable selection is valid even if the number of variables is large. The selection consistency is obtained and finite performances are illustrated via Monte Carlo experiments.

In binary and ordinal response models outlying covariates as well as incoherent responses may affect the reliability of the maximum likelihood estimators and that of the derived inferential procedures. However the various link functions, which provide the relationship between the linear predictor and the probabilities of the response categories, differ in terms of sensitivity to anomalous data. The current paper derives conditions useful to evaluate the properties of the link functions with respect to robustness, either when the covariates are outlier free or when extreme design points may occur. The main results show that – by an appropriate choice of the link function – robust estimators, with a bounded influence function, can be easily derived from the usual likelihood function, while preserving the predictive ability of the fitted model.

A receiver operating characteristic (ROC) curve based on the Lehmann family of distributions has a very simple form and is an important alternative to the popular binormal ROC curve. In this paper, we propose to use the minimum distance method to estimate a one-dimensional parameter of this curve. We prove the consistency and asymptotic normality of estimators obtained by applying various measures of discrepancy. In a simulation study, we compare the accuracy of the estimators proposed with the accuracy of a known estimator based on a partial likelihood method and an estimator based on the estimation of the area under the curve. We also provide an illustrative example of an application to real data.

ABSTRACT Quantile regression (QR) is a well-established method of tail analysis. Application of QR can become very challenging when dealing with high-dimensional data, thus requiring dimension reduction techniques. While the current literature on these techniques focuses on extracting linear combinations of the predictor variables that contain all the information about the conditional quantile, non-linear features can potentially achieve greater dimension reduction. We, therefore, present the first application of transformed dimension reduction for conditional quantiles, which serves as an intermediate step between linear and nonlinear dimension reduction. The idea is to transform the predictors monotonically and then look for low-dimensional projections by applying linear dimension reduction techniques. The performance of the proposed methodology is demonstrated through simulation examples and a real data application.

Discrete choice experiments are a popular method to measure part worths of economic goods and in health science. These models include several attributes as explanatory variables. The commonly used multinomial logit model assumes independent utilities for different choice options. In Graßhoff et al. [Optimal design for discrete choice experiments. J Statist Plann Inference. 2013;143:167–175] we pointed out that for such a model designs turn out to be formally optimal which may comprise choice sets containing identical or nearly identical options and which are not reasonable for use in empirical discrete choice studies. To overcome this problem we introduce a novel model based on probit part-worth utilities which can account for similarities in the alternatives by supposing a dependence structure. For this model we derive locally D-optimal designs which appear to be more reasonable for applications.

ABSTRACT We introduce a new variable selection method, called SgenoLasso, that handles extreme data. Our method relies on the construction of a specific statistical test, a transformation of the data and by the knowledge of the correlation between regressors. It is appropriate in genomics since once the genetic map has been built, the correlation is perfectly known. This new technique is inspired by stochastic processes arising from statistical genetics. We prove that the signal to noise ratio is largely increased by considering the extremes. Our approach and existing methods are compared on simulated and real data, and the results point to the validity of our approach.

The consistency of the jackknife estimator of the asymptotic covariance matrix of a differentiable function of the symmetrized Tyler matrix is proved for sampling from continuous distribution without any constraint on this sampled continuous distribution. It is shown that under mild regularity conditions the rank of the asymptotic covariance matrix attains maximum possible value. The results are applied to the construction of the asymptotic confidence interval for correlation coefficient. It is illustrated by simulations that for some distributions the proposed interval yields better results than the classical Z-transformation interval.

This paper describes two tests in the growth curve model under multivariate normality. The first one is revisited test for intraclass structure of the covariance matrix, and the second one is the simultaneous test for intraclass covariance structure together with a specific mean value of the model. Both tests are likelihood ratio tests.

51 definition continuous case 30 definition discrete case 28 Empirical 143 Uniform (discrete) 28 Central Limit Theorem 50, 75, 76 MLE asymptotics 90 proof 76 CF, see Characteristic function 38 Change of variables 57 bivariate calculus method 60 Box-Mller transformation 61 calculus method 59 direct method 57 Characteristic function 38 Chebyshev's inequality 69 Chi-squared distribution, see PDF 43 Chi-squared test 113, 118, 120 CI, see Confidence intervals 113 CLT, see Central Limit Theorem 75 Combination 151 Combination coefficient 20 multinomial 22,

The field of statistics has a rich history that has become tightly integrated into the emerging field of data sciences. Collaboration with computer scientists, numerical analysts, and decision makers characterizes the field. The mathematical backbone of all of the statistical methods is probability theory. This chapter discusses the basics of probability theory and random variables. It also studies the statistical methods and the basics of statistical decision theory. Finding structure in data is a primary goal of data science. Graphical methods are powerful approaches to discovering unexpected or hidden structure. Some of these methods are better suited to small datasets. The fundamental task of statistics is prediction. Data for this task are typically ordered pairs. The goal is to predict the value of the y variable using the corresponding value of the x variable.