Título: A three-step approach to production frontier estimation and the Matsuoka’s distribution.
Resumo: In this work, we introduce a three-step semiparametric methodology for the estimation of production frontiers. We consider a model inspired by the well-known Cobb-Douglas production function, wherein input factors operate multiplicatively within the model. Efficiency in the proposed model is assumed to follow a continuous univariate uniparametric distribution in (0,1), referred to as Matsuoka’s distribution, which is discussed in detail. Following model linearization, the first step is to nonparametrically estimate the regression function through a local linear smoother. The second step focuses on the estimation of the efficiency parameter. Finally, we estimate the production frontier through a plug-in methodology. We present a rigorous asymptotic theory related to the proposed three-step estimation, including consistency, and asymptotic normality, and derive rates for the convergences presented. Incidentally, we also study the Matsuoka’s distribution, deriving its main properties. The Matsuoka’s distribution exhibits a versatile array of shapes capable of effectively encapsulating the typical behavior of efficiency within production frontier models. To complement the large sample results obtained, a Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed three-step methodology. An empirical application using a dataset of Danish milk producers is also presented.
Palestrante: Danilo Matsuoka
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Título: NEW GENERALIZED AUTOREGRESSIVE SCORE MODELS: FORECASTING SUSTAINABLE DEVELOPMENT INDICATORS
Resumo: In this work, we aim to propose new models that combine the conditional distributions of Unit Gamma (UG) and Burr XII (BXII) with the class of Generalized Autoregressive Score (GAS) models, named UG-GAS and BXII-GAS. This proposal aims to enhance understanding of stochastic behavior and forecast sustainable development indicators related to the United Nations Sustainable Development Goals (SDGs). UG is a bi-parametric distribution limited to the unit interval, widely applied in fields such as biology and hydrology. The BXII distribution offers the advantage of representing asymmetric behaviors in positive random variables, making it suitable for various applications in fields such as remote sensing, econometrics, environmental science, and extreme event analysis in hydroclimatology. Dynamic structures can be employed to model time-dependent effects. In this context, GAS models provide a useful framework. They update time-varying parameters based on past observations and the weighted score function, considering the complete structure of the predictive distribution in parameter updates. Conditional maximum likelihood estimators are used to estimate the parameters of the proposed models. A Monte Carlo simulation study was conducted using different finite sample sizes to assess the performance of point and interval estimators. The proposed models are applied to real data on capacity factors in wind farms, and river flows in hydroelectric power plants and are compared with other models known in the literature.
Palestrante: Fernando Jose Monteiro de Araujo
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Título: Podemos colar séries temporais?
Resumo: A pandemia de Covid-19 causou interrupções significativas em diversas pesquisas, incluindo aquelas realizadas pelo CECLIMAR/UFRGS. Os pesquisadores coletaram dados semanais sobre a Descarga de Água Subterrânea (DAS) durante 40 semanas antes da pandemia, mas tiveram que suspender as coletas por dois anos. Com o fim da pandemia, retomaram as coletas e agora buscam entender se é possível combinar os dados anteriores com os novos para criar um banco de dados maior. O trabalho atual visa estabelecer a base teórica para a “colagem” de séries temporais, começando pela aplicação do teorema do limite central a processos AR(q) acoplados.
Palestrante: Lucas Pasqualin Cantu
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Data: 17/09/2024
Horário: 13h30min
Local: Sala A101 do Instituto de Matemática e Estatística da UFRGS (Av. Bento Gonçalves, 9500 Prédio 43-111)