656 research outputs found
Large-sample estimation and inference in multivariate single-index models
By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indee
A particle method for the homogeneous Landau equation
We propose a novel deterministic particle method to numerically approximate
the Landau equation for plasmas. Based on a new variational formulation in
terms of gradient flows of the Landau equation, we regularize the collision
operator to make sense of the particle solutions. These particle solutions
solve a large coupled ODE system that retains all the important properties of
the Landau operator, namely the conservation of mass, momentum and energy, and
the decay of entropy. We illustrate our new method by showing its performance
in several test cases including the physically relevant case of the Coulomb
interaction. The comparison to the exact solution and the spectral method is
strikingly good maintaining 2nd order accuracy. Moreover, an efficient
implementation of the method via the treecode is explored. This gives a proof
of concept for the practical use of our method when coupled with the classical
PIC method for the Vlasov equation.Comment: 27 pages, 14 figures, debloated some figures, improved explanations
in sections 2, 3, and
Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM
In this paper, we investigate the convergence and consistency properties of
an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization
and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm
are proven. These proofs do not require the restrictive assumption that the
Jacobians of the motion and observation models need to be evaluated at the
ground truth. It is also shown that the output of RI-EKF is invariant under any
stochastic rigid body transformation in contrast to based EKF
SLAM algorithm (-EKF) that is only invariant under
deterministic rigid body transformation. Implications of these invariance
properties on the consistency of the estimator are also discussed. Monte Carlo
simulation results demonstrate that RI-EKF outperforms -EKF,
Robocentric-EKF and the "First Estimates Jacobian" EKF, for 3D point feature
based SLAM
Depressive Symptoms and Obesity/Weight Gain Factors Among Black and Hispanic Pregnant Women
This study examined the relationships between depressive symptoms and obesity/weight gain factors in 56 Black and Hispanic pregnant women and the differences in these variables between the 2 ethnic groups. Of the women, 32% were likely depressed, 66% were overweight/obese, and 45% gained excessive gestational weight. Depressive symptoms were positively correlated with prepregnancy body mass index (BMI; r = .268, p = .046), inversely related to gestational weight gain (r = –.329, p = .013), and not associated with excessive gestational weight gain. Black women were more likely to have excessive gestational weight gain than Hispanic women. Prepregnancy BMI and gestational weight gain data can be useful in identifying pregnant women with depression
Single-index regression models
Indiana University-Purdue University Indianapolis (IUPUI)Useful medical indices pose important roles in predicting medical outcomes. Medical indices, such as the well-known Body Mass Index (BMI), Charleson Comorbidity Index, etc., have been used extensively in research and clinical practice, for the quantification of risks in individual patients. However, the development of these indices is challenged; and primarily based on heuristic arguments. Statistically, most medical indices can be expressed as a function of a linear combination of individual variables and fitted by single-index model. Single-index model represents a way to retain latent nonlinear features of the data without the usual complications that come with increased dimensionality. In my dissertation, I propose a single-index model approach to analytically derive indices from observed data; the resulted index inherently correlates with specific health outcomes of interest. The first part of this dissertation discusses the derivation of an index function for the prediction of one outcome using longitudinal data. A cubic-spline estimation scheme for partially linear single-index mixed effect model is proposed to incorporate the within-subject correlations among outcome measures contributed by the same subject. A recursive algorithm based on the optimization of penalized least square estimation equation is derived and is shown to work well in both simulated data and derivation of a new body mass measure for the assessment of hypertension risk in children. The second part of this dissertation extends the single-index model to a multivariate setting. Specifically, a multivariate version of single-index model for longitudinal data is presented. An important feature of the proposed model is the accommodation of both correlations among multivariate outcomes and among the repeated measurements from the same subject via random effects that link the outcomes in a unified modeling structure. A new body mass index measure that simultaneously predicts systolic and diastolic blood pressure in children is illustrated. The final part of this dissertation shows existence, root-n strong consistency and asymptotic normality of the estimators in multivariate single-index model under suitable conditions. These asymptotic results are assessed in finite sample simulation and permit joint inference for all parameters
- …