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García Pérez, Alfonso

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García Pérez
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2019 - 201912020 - 20233
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Mostrando 1 - 4 de 4
  • Miniatura
    Publicación
    On robustness for spatio-temporal data
    (MDPI, 2022-05-23) García Pérez, Alfonso
    The spatio-temporal variogram is an important factor in spatio-temporal prediction through kriging, especially in fields such as environmental sustainability or climate change, where spatio-temporal data analysis is based on this concept. However, the traditional spatio-temporal variogram estimator, which is commonly employed for these purposes, is extremely sensitive to outliers. We approach this problem in two ways in the paper. First, new robust spatio-temporal variogram estimators are introduced, which are defined as M-estimators of an original data transformation. Second, we compare the classical estimate against a robust one, identifying spatio-temporal outliers in this way. To accomplish this, we use a multivariate scale-contaminated normal model to produce reliable approximations for the sample distribution of these new estimators. In addition, we define and study a new class of M-estimators in this paper, including real-world applications, in order to determine whether there are any significant differences in the spatio-temporal variogram between two temporal lags and, if so, whether we can reduce the number of lags considered in the spatio-temporal analysis.
  • Miniatura
    Publicación
    A New Estimator: Median of the Distribution of the Mean in Robustness
    (MDPI, 2023-06-14) García Pérez, Alfonso
    In some statistical methods, the statistical information is provided in terms of the values used by classical estimators, such as the sample mean and sample variance. These estimations are used in a second stage, usually in a classical manner, to be combined into a single value, as a weighted mean. Moreover, in many applied studies, the results are given in these terms, i.e., as summary data. In all of these cases, the individual observations are unknown; therefore, computing the usual robustness estimators with them to replace classical non-robust estimations by robust ones is not possible. In this paper, the use of the median of the distribution 𝐹𝑥̲ of the sample mean is proposed, assuming a location-scale contaminated normal model, where the parameters of 𝐹𝑥̲ are estimated with the classical estimations provided in the first stage. The estimator so defined is called median of the distribution of the mean, 𝑀𝑑𝑀. This new estimator is applied in Mendelian randomization, defining the new robust inverse weighted estimator, RIVW.
  • Miniatura
    Publicación
    New robust cross-variogram estimators and approximations of their distributions based on saddlepoint techniques
    (MDPI, 2021-04-01) García Pérez, Alfonso
    Let 𝐙(𝐬)=(𝑍1(𝐬),…,𝑍𝑝(𝐬))𝑡 be an isotropic second-order stationary multivariate spatial process. We measure the statistical association between the p random components of 𝐙 with the correlation coefficients and measure the spatial dependence with variograms. If two of the 𝐙 components are correlated, the spatial information provided by one of them can improve the information of the other. To capture this association, both within components of 𝐙(𝐬)and across 𝐬, we use a cross-variogram. Only two robust cross-variogram estimators have been proposed in the literature, both by Lark, and their sample distributions were not obtained. In this paper, we propose new robust cross-variogram estimators, following the location estimation method instead of the scale estimation one considered by Lark, thus extending the results obtained by García-Pérez to the multivariate case. We also obtain accurate approximations for their sample distributions using saddlepoint techniques and assuming a multivariate-scale contaminated normal model. The question of the independence of the transformed variables to avoid the usual dependence of spatial observations is also considered in the paper, linking it with the acceptance of linear variograms and cross-variograms.
  • Miniatura
    Publicación
    Saddlepoint approximations for the distribution of some robust estimators of the variogram
    (Springer, 2019-06-26) García Pérez, Alfonso
    In this paper, we obtain a saddlepoint approximation for the small sample distribution of several variogram estimators such as the classical Matheron’s estimator, some M-estimators like the robust Huber’s variogram estimator, and also the α-trimmed variogram estimator. The tail probability approximation obtained is very accurate even for small sample sizes. In the approximations we consider that the observations follow a distribution close to the normal, specifically, a scale contaminated normal model. To obtain the approximations we transform the original observations into a new ones, which can be considered independent if a linearized variogram can be accepted as model for them. To check this, a goodness of fit test for a variogram model is defined in the last part of the paper.