Estimating linear functionals in nonlinear regression with responses missing at random

We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate expectations of functions of covariate and response we use a fully imputed estimator, namely an empirical estimator based on estimators of conditional expectations given the covariate. We exploit the independence of covariates and errors by writing the conditional expectations as unconditional expectations, which can now be estimated by empirical plug-in estimators. The mean zero constraint on the error distribution is exploited by adding suitable residual-based weights. We prove that the estimator is efficient (in the sense of H\'{a}jek and Le Cam) if an efficient estimator of the parameter is used. Our results give rise to new efficient estimators of smooth transformations of expectations. Estimation of the mean response is discussed as a special (degenerate) case.Comment: Published in at http://dx.doi.org/10.1214/08-AOS642 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference about the slope in linear regression: an empirical likelihood approach

We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719, 2017), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study

Efficient prediction for linear and nonlinear autoregressive models

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.Comment: Published at http://dx.doi.org/10.1214/009053606000000812 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimality of estimators for misspecified semi-Markov models

Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two models for the process are semiparametric, and the parameters can be estimated by conditional maximum likelihood estimators. The third model for the process is parametric, and the parameter can be estimated by an unconditional maximum likelihood estimator. We determine heuristically the asymptotic distributions of these estimators and show that they are asymptotically efficient. If the parametric models are not correct, the (conditional) maximum likelihood estimators estimate the parameter that maximizes the Kullback--Leibler information. We show that they remain asymptotically efficient in a nonparametric sense.Comment: To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm

Using New Camera-Based Technologies for Gait Analysis in Older Adults in Comparison to the Established GAITRite System

Various gait parameters can be used to assess the risk of falling in older adults. However, the state-of-the-art systems used to quantify gait parameters often come with high costs as well as training and space requirements. Gait analysis systems, which use mobile and commercially available cameras, can be an easily available, marker-free alternative. In a study with 44 participants (age ≥ 65 years), gait patterns were analyzed with three different systems: a pressure sensitive walkway system (GAITRite-System, GS) as gold standard, Motognosis Labs Software using a Microsoft Kinect Sensor (MKS), and a smartphone camera-based application (SCA). Intertrial repeatability showed moderate to excellent results for MKS (ICC(1,1) 0.574 to 0.962) for almost all measured gait parameters and moderate reliability in SCA measures for gait speed (ICC(1,1) 0.526 to 0.535). All gait parameters of MKS showed a high level of agreement with GS (ICC(2,k) 0.811 to 0.981). Gait parameters extracted with SCA showed poor reliability. The tested gait analysis systems based on different camera systems are currently only partially able to capture valid gait parameters. If the underlying algorithms are adapted and camera technology is advancing, it is conceivable that these comparatively simple methods could be used for gait analysis

Gleichheit im Zeitalter der Differenz: einige methodologische Erwägungen zur Frauenforschung

Die Arbeit thematisiert 'Gleichheit' und Differenz im Rahmen der Androzentrismuskritik als methodologisches Problem, seine Bedeutung für die empirische Forschung und deren Gegenstandsbezug in feministischer Sicht. Schwerpunktmäßig setzt sich die Autorin mit dem Vorwurf von männlichen Wissenschaftlern auseinander, Frauen seien zu keiner wissenschaftlichen Objektivität fähig. In diesem Zusammenhang wird die 'Sicht von unten'-Perspektive feministischer Forschung als Stabilisierungshilfe für die gegebenen gesellschaftlichen Geschlechterdifferenzen kritisiert und eine grenzüberschreitende 'Sicht-von der-Seite'-Perspektive vorgeschlagen. Zusammenfassend wird das Problem hervorgehoben, Gleichheit in einer auf Geschlechterdifferenzierung basierenden Wissenschaft durchzusetzen und das Stadium gegenseitiger Verachtung zu überwinden. Die Arbeit basiert auf der Verwertung von Sekundärquellen. (ICB