arXiv subjects

Maikol Solís

Publications and source records attributed to Maikol Solís.

6 recordsLinked to original sources

arXiv2021

Using relative weight analysis with residualization to detect relevant nonlinear interaction effects in ordinary and logistic regressions

Relative weight analysis is a classic tool for detecting whether one variable or interaction in a model is relevant. In this study, we focus on the construction of relative weights for non-linear interactions using restricted cubic splines. Our aim is to provide an accessible method to analyze a multivariate model and identify one subset with the most representative set of variables. Furthermore, we developed a procedure for treating control, fixed, free and interaction terms simultaneously in the residual weight analysis. The interactions are residualized properly against their main effects to maintain their true effects in the model. We tested this method using two simulated examples.

stat.ME↗

arXiv2020

Geometric goodness of fit measure to detect patterns in data point clouds

We derived a geometric goodness-of-fit index, similar to $R^2$ using topological data analysis techniques. We build the Vietoris-Rips complex from the data-cloud projected onto each variable. Estimating the area of the complex and their domain, we create an index that measures the emptiness of the space with respect to the data. We made the analysis with an own package called TopSA (Topological Sensitivy Analysis).

stat.CO↗

arXiv2020

Estimation of first-order sensitivity indices based on symmetric reflected Vietoris-Rips complexes areas

In this paper we estimate the first-order sensitivity index of random variables within a model by reconstructing the embedding manifold of a two-dimensional cloud point. The model assumed has p predictors and a continuous outcome Y . Our method gauges the manifold through a Vietoris-Rips complex with a fixed radius for each variable. With this object, and using the area and its symmetric reflection, we can estimate an index of relevance for each predictor. The index reveals the geometric nature of the data points. Also, given the method used, we can decide whether a pair of non-correlated random variables have some structural pattern in their interaction.

math.ST↗

arXiv2019

Nonparametric estimation of the first order Sobol indices with bootstrap bandwidth

Suppose that $Y = ψ(X_1, \ldots, X_p)$, where $(X_1,\ldots, X_p)^\top$ are random inputs, $Y$ is the output, and $ψ(\cdot)$ is an unknown link function. The Sobol indices gauge the sensitivity of each $X$ against $Y$ by estimating the regression curve's variability between them. In this paper, we estimate these curves with a kernel-based method. The method allows to estimate the first order indices when the link between the independent and dependent variables is unknown. The kernel-based methods need a bandwidth to average the observations. For finite samples, the cross-validation method is famous to decide this bandwidth. However, it produces a structural bias. To remedy this, we propose a bootstrap procedure which reconstruct the model residuals and re-estimate the non-parametric regression curve. With the new set of curves, the procedure corrects the bias in the Sobol index. To test the developed method, we implemented simulated numerical examples with complex functions.

stat.ME↗

arXiv2018

Rates of convergence in conditional covariance matrix with nonparametric entries estimation

Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ applying a plug-in kernel-based algorithm to its entries. Next, we investigate the estimators rate of convergence under smoothness hypotheses on the density function of $(\boldsymbol{X},Y)$. In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ entries. We illustrate a sliced inverse regression setting for time series matching the conditions of our estimator

stat.ME↗

arXiv2014

Efficient estimation of conditional covariance matrices for dimension reduction

Let $\boldsymbol{X}\in \mathbb{R}^p$ and $Y\in \mathbb{R}$. In this paper we propose an estimator of the conditional covariance matrix, $\mathrm{Cov}(\mathbb{E}[\boldsymbol{X}\vert Y])$, in an inverse regression setting. Based on the estimation of a quadratic functional, this methodology provides an efficient estimator from a semi parametric point of view. We consider a functional Taylor expansion of $\mathrm{Cov}(\mathbb{E}[\boldsymbol{X}\vert Y])$ under some mild conditions and the effect of using an estimate of the unknown joint distribution. The asymptotic properties of this estimator are also provided.

math.ST↗