Marta Sestelo

Variable selection in regression models used to analyse Global Positioning System accuracy in forest environments

Abstract Reliable information on the geographic location of individual points using GPS (Global Positioning System) receivers requires an unobstructed line of sight from the points to a minimum of four satellites. This is often difficult to achieve in forest environments, as trunks, branches and leaves can block the GPS signal. Forest canopy can be characterized by means of dasymetric parameters such as tree density and biomass volume, but it is important to know which parameters in particular have a bearing on the accuracy of GPS measurements. We analyzed the relative influence of forest canopy and GPS-signal-related variables on the accuracy of the GPS observations using a methodology based on linear regression models and bootstrapping and compared the results to those for a classical variable-selection method based on hypothesis testing. The results reveal that our methodology reduces the number of significant variables by approximately 50% and that both forestry and GPS-signal-related variables are significant.

A method for determining groups in multiple survival curves: A Method for Determining Groups in Multiple Survival Curves

Survival analysis includes a wide variety of methods for analyzing time-to-event data. One basic but important goal in survival analysis is the comparison of survival curves between groups. Several nonparametric methods have been proposed in the literature to test for the equality of survival curves for censored data. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, it can be interesting to ascertain whether curves can be grouped or if all these curves are different from each other. A method is proposed that allows determining groups with an automatic selection of their number. The validity and behavior of the proposed method was evaluated through simulation studies. The applicability of the proposed method is illustrated using real data. Software in the form of an R package has been developed implementing the proposed method.

Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions, and the conditional distribution of gap times. In this work, we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a dataset from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

An R Package For Analyzing Factor‐By‐Curve Interactions

Analysis of such studies can be successfully performed using nonparametric regression models. In the nonparametric regression framework, issues of interest include the so‐called factor‐by‐curve interaction, where the effect of a continuous covariate on response varies across groups defined by levels of a categorical variable. This study sought to compare regression curves and their derivatives that may vary across groups defined by different experimental conditions. For this purpose, we propose the use of local linear kernel smoothers. This study introduces a software application for R which performs inference in a nonparametric regression model. It describes the capabilities of the program for estimating these models (and their derivatives) and for drawing different regression curves by factor levels. The main feature of the package is its ability to draw inferences about critical points, such as maxima or change points linked to the derivative curves. Bootstrap methods were implemented to draw inference...

Selecting Variables in Regression Models. A New Approach to the Prediction of Time Series of S O2

A question that tends to arise in multiple regression models (with p variables), and that has not been totally satisfactory solved, is to determine the best subset or subsets of q q≤p) predictors which will establish the model or models with the best discrimination capacity. This problem is particularly important where p is high and/or where there are mutually redundant predictors. With this work, we present a new approach to this problem, where we will try to predict a new emission episode of S O2, but focusing our attention in the importance to know the best combinations of time instants to obtain the best prediction. The proposed method is a new forward stepwise‐based selection procedure that selects a model containing a subset of variables (or time instants) according to an optimal criteria (determination coefficient or Akaike Information Criterion) and taking into account the computational cost. Additionally, bootstrap resampling techniques are used to implement tests capable of detecting whether sig...