Epsilon Birnbaum–Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum–Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427–443, 2005). The extension allows generating Birnbaun–Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88–95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.     

Simultaneous marginal survival estimators when doubly censored data is present

A doubly censoring scheme occurs when the lifetimes T being measured, from a well-known time origin, are exactly observed within a window [L, R] of observational time and are otherwise censored either from above (right-censored observations) or below (left-censored observations). Sample data consists on the pairs (U, δ) where U = min{R, max{T, L}} and δ indicates whether T is exactly observed (δ = 0), right-censored (δ = 1) or left-censored (δ = −1). We are interested in the estimation of the marginal behaviour of the three random variables T, L and R based on the observed pairs (U, δ). We propose new nonparametric simultaneous marginal estimators [^(S)]_T, [^(S)]_L{\hat S_{T}, \hat S_{L}} and [^(S)]_R{\hat S_{R}} for the survival functions of T, L and R, respectively, by means of an inverse-probability-of-censoring approach. The proposed estimators [^(S)]_T, [^(S)]_L{\hat S_{T}, \hat S_{L}} and [^(S)]_R{\hat S_{R}} are not computationally intensive, generalize the empirical survival estimator and reduce to the Kaplan-Meier estimator in the absence of left-censored data. Furthermore, [^(S)]_T{\hat S_{T}} is equivalent to a self-consistent estimator, is uniformly strongly consistent and asymptotically normal. The method is illustrated with data from a cohort of drug users recruited in a detoxification program in Badalona (Spain). For these data we estimate the survival function for the elapsed time from starting IV-drugs to AIDS diagnosis, as well as the potential follow-up time. A simulation study is discussed to assess the performance of the three survival estimators for moderate sample sizes and different censoring levels.     

A two-sample empirical likelihood ratio test based on samples entropy

Powerful entropy-based tests for normality, uniformity and exponentiality have been well addressed in the statistical literature. The density-based empirical likelihood approach improves the performance of these tests for goodness-of-fit, forming them into approximate likelihood ratios. This method is extended to develop two-sample empirical likelihood approximations to optimal parametric likelihood ratios, resulting in an efficient test based on samples entropy. The proposed and examined distribution-free two-sample test is shown to be very competitive with well-known nonparametric tests. For example, the new test has high and stable power detecting a nonconstant shift in the two-sample problem, when Wilcoxon’s test may break down completely. This is partly due to the inherent structure developed within Neyman-Pearson type lemmas. The outputs of an extensive Monte Carlo analysis and real data example support our theoretical results. The Monte Carlo simulation study indicates that the proposed test compares favorably with the standard procedures, for a wide range of null and alternative distributions.     

A note on the asymptotic distribution of a Perron-type innovational outlier unit root test with a break

This note provides the asymptotic distribution of a Perron-type innovational outlier unit root test developed by Popp (J Stat Comput Sim 78:1145–1161, 2008) in case of a shift in the intercept for non-trending data. In Popp (J Stat Comput Sim 78:1145–1161, 2008), only critical values for finite samples based on Monte Carlo techniques are tabulated. Using similar arguments as in Zivot and Andrews (J Bus Econ Stat 10:251–270, 1992), weak convergence is shown for the test statistics.     

Automatic estimation procedure in partial linear model with functional data

Partial linear modelling ideas have recently been adapted to situations when functional data are observed. This paper aims to complete the study of such model by proposing a fully automatic estimation procedure. This is achieved by constructing a data-driven method to choose the smoothing parameters entered in the nonparametric components of the model. The asymptotic optimality of the method is stated and its practical interest is illustrated on finite size Monte Carlo simulated samples.     

Longitudinal dynamic analyses of cognition in the health and retirement study panel

The purpose of this paper is to highlight some classic issues in the measurement of change and to show how contemporary solutions can be used to deal with some of these issues. Five classic issues will be raised here: (1) Separating individual changes from group differences; (2) options for incomplete longitudinal data over time, (3) options for nonlinear changes over time; (4) measurement invariance in studies of changes over time; and (5) new opportunities for modeling dynamic changes. For each issue we will describe the problem, and then review some contemporary solutions to these problems base on Structural Equation Models (SEM). We will fit these SEM to using existing panel data from the Health & Retirement Study (HRS) cognitive variables. This is not intended as an overly technical treatment, so only a few basic equations are presented, examples will be displayed graphically, and more complete references to the contemporary solutions will be given throughout.     

Penalized least absolute deviations estimation for nonlinear model with change-points

This paper studies the asymptotic properties of a smoothed least absolute deviations estimator in a nonlinear parametric model with multiple change-points occurring at the unknown times with independent and identically distributed errors. The model is nonlinear in the sense that between two successive change-points the regression function is nonlinear into respect to parameters. It is shown via Monte Carlo simulations that its performance is competitive with that of least absolute deviations estimator and it is more efficient than the least squares estimator, particularly in the presence of the outlier points. If the number of change-points is unknown, an estimation criterion for this number is proposed. Interest of this method is that the objective function is approximated by a differentiable function and if the model contains outliers, it detects correctly the location of the change-points.