Asta-Advances in Statistical Analysis最新文献

The extreme value theory (EVT) encompasses a set of methods that allow inferring about the risk inherent to various phenomena in the scope of economic, financial, actuarial, environmental, hydrological, climatic sciences, as well as various areas of engineering. In many situations the clustering effect of high values may have an impact on the risk of occurrence of extreme phenomena. For example, extreme temperatures that last over time and result in drought situations, the permanence of intense rains leading to floods, stock markets in successive falls and consequent catastrophic losses. The extremal index is a measure of EVT associated with the degree of clustering of extreme values. In many situations, and under certain conditions, it corresponds to the arithmetic inverse of the average size of high-value clusters. The estimation of the extremal index generally entails two sources of uncertainty: the level at which high observations are considered and the identification of clusters. There are several contributions in the literature on the estimation of the extremal index, including methodologies to overcome the aforementioned sources of uncertainty. In this work we will revisit several existing estimators, apply automatic choice methods, both for the threshold and for the clustering parameter, and compare the performance of the methods. We will end with an application to meteorological data.

This paper proposes an M-quantile regression approach to address the heterogeneity of the housing market in a modern European city. We show how M-quantile modelling is a rich and flexible tool for empirical market price data analysis, allowing us to obtain a robust estimation of the hedonic price function whilst accounting for different sources of heterogeneity in market prices. The suggested methodology can generally be used to analyse nonlinear interactions between prices and predictors. In particular, we develop a spatial semiparametric M-quantile model to capture both the potential nonlinear effects of the cultural environment on pricing and spatial trends. In both cases, nonlinearity is introduced into the model using appropriate bases functions. We show how the implicit price associated with the variable that measures cultural amenities can be determined in this semiparametric framework. Our findings show that the effect of several housing attributes and urban amenities differs significantly across the response distribution, suggesting that buyers of lower-priced properties behave differently than buyers of higher-priced properties.

Many real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter (alpha) is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of (alpha), with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example.

Communication through websites is often characterised by short texts, made of few words, such as image captions or tweets. This paper explores the class of supervised learning methods for the analysis of short texts, as an alternative to unsupervised methods, widely employed to infer topics from structured texts. The aim is to assess the effectiveness of text data in social sciences, when they are used as explanatory variables in regression models. To this purpose, we compare different variable selection procedures when text regression models are fitted to real, short, text data. We discuss the results obtained by several variants of lasso, screening-based methods and randomisation-based models, such as sure independence screening and stability selection, in terms of number and importance of selected variables, assessed through goodness-of-fit measures, inclusion frequency and model class reliance. Latent Dirichlet allocation results are also considered as a term of comparison. Our perspective is primarily empirical and our starting point is the analysis of two real case studies, though bootstrap replications of each dataset are considered. The first case study aims at explaining price variations based on the information contained in the description of items on sale on e-commerce platforms. The second regards open questions in surveys on satisfaction ratings. The case studies are different in nature and representative of different kinds of short texts, as, in one case, a concise descriptive text is considered, whereas, in the other case, the text expresses an opinion.

While the vaccination campaign against COVID-19 is having its positive impact, we retrospectively analyze the causal impact of some decisions made by the Italian government on the second outbreak of the SARS-CoV-2 pandemic in Italy, when no vaccine was available. First, we analyze the causal impact of reopenings after the first lockdown in 2020. In addition, we also analyze the impact of reopening schools in September 2020. Our results provide an unprecedented opportunity to evaluate the causal relationship between the relaxation of restrictions and the transmission in the community of a highly contagious respiratory virus that causes severe illness in the absence of prophylactic vaccination programs. We present a purely data-analytic approach based on a Bayesian methodology and discuss possible interpretations of the results obtained and implications for policy makers.

From the inventory of the health insurer AOK in 2004, we draw a sample of a quarter million people and follow each person’s health claims continuously until 2013. Our aim is to estimate the effect of a stroke on the dementia onset probability for Germans born in the first half of the 20th century. People deceased before 2004 are randomly left-truncated, and especially their number is unknown. Filtrations, modelling the missing data, enable circumventing the unknown number of truncated persons by using a conditional likelihood. Dementia onset after 2013 is a fixed right-censoring event. For each observed health history, Jacod’s formula yields its conditional likelihood contribution. Asymptotic normality of the estimated intensities is derived, related to a sample size definition including the number of truncated people. The standard error results from the asymptotic normality and is easily computable, despite the unknown sample size. The claims data reveal that after a stroke, with time measured in years, the intensity of dementia onset increases from 0.02 to 0.07. Using the independence of the two estimated intensities, a 95% confidence interval for their difference is [0.053, 0.057]. The effect halves when we extend the analysis to an age-inhomogeneous model, but does not change further when we additionally adjust for multi-morbidity.

Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for sparse deep learning. In contrast to previous work, we consider different types of sparsity, such as few active connections, few active nodes, and other norm-based types of sparsity. Moreover, our theories cover important aspects that previous theories have neglected, such as multiple outputs, regularization, and (ell_{2})-loss. The guarantees have a mild dependence on network widths and depths, which means that they support the application of sparse but wide and deep networks from a statistical perspective. Some of the concepts and tools that we use in our derivations are uncommon in deep learning and, hence, might be of additional interest.

The main aim of this paper is to propose a set of tools for assessing non-normality taking into consideration the class of multivariate t-distributions. Assuming second moment existence, we consider a reparameterized version of the usual t distribution, so that the scale matrix coincides with covariance matrix of the distribution. We use the local influence procedure and the Kullback–Leibler divergence measure to propose quantitative methods to evaluate deviations from the normality assumption. In addition, the possible non-normality due to the presence of both skewness and heavy tails is also explored. Our findings based on two real datasets are complemented by a simulation study to evaluate the performance of the proposed methodology on finite samples.

Ridge regression estimators can be interpreted as a Bayesian posterior mean (or mode) when the regression coefficients follow multivariate normal prior. However, the multivariate normal prior may not give efficient posterior estimates for regression coefficients, especially in the presence of interaction terms. In this paper, the vine copula-based priors are proposed for Bayesian ridge estimators under the Cox proportional hazards model. The semiparametric Cox models are built on the posterior density under two likelihoods: Cox’s partial likelihood and the full likelihood under the gamma process prior. The simulations show that the full likelihood is generally more efficient and stable for estimating regression coefficients than the partial likelihood. We also show via simulations and a data example that the Archimedean copula priors (the Clayton and Gumbel copula) are superior to the multivariate normal prior and the Gaussian copula prior.