A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

The bias in reversing the Box-Cox transformation in time series forecasting: An empirical study based on neural networks

The Box-Cox transformation is a technique mostly utilized to turn the probabilistic distribution of a time series data into approximately normal. And this helps statistical and neural models to perform more accurate forecastings. However, it introduces a bias when the reversion of the transformation is conducted with the predicted data. The statistical methods to perform a bias-free reversion require, necessarily, the assumption of Gaussianity of the transformed data distribution, which is a rare event in real-world time series. So, the aim of this study was to provide an effective method of removing the bias when the reversion of the Box-Cox transformation is executed. Thus, the developed method is based on a focused time lagged feedforward neural network, which does not require any assumption about the transformed data distribution. Therefore, to evaluate the performance of the proposed method, numerical simulations were conducted and the Mean Absolute Percentage Error, the Theil Inequality Index and the Signal-to-Noise ratio of 20-step-ahead forecasts of 40 time series were compared, and the results obtained indicate that the proposed reversion method is valid and justifies new studies. (C) 2014 Elsevier B.V. All rights reserved.

A demanda por moeda no Brasil no período 1974-2008: estimativas sob expectativas adaptativas e racionais

O objetivo principal desta dissertação é analisar a demanda por moeda no Brasil no período 1974 a 2008, lembrando que ele inclui sub-períodos de inflação elevada, e baixa, e levando em conta hipóteses alternativas quanto à formação de expectativas. A especificação adotada é a de Tourinho (1995), que generaliza a de Cagan (1956) para permitir uma forma funcional mais flexível e incorporar outras variáveis, além da inflação esperada, como variáveis explicativas. Verifica-se que estas extensões são importantes para modelar a demanda por saldos monetários reais no período aqui considerado. A forma funcional semi-log de Cagan é rejeitada, em favor de uma forma funcional flexível Box-Cox, e os coeficientes da taxa de juros real e da variância da inflação são significativos, mostrando a importância destas variáveis serem inseridas ao modelo. A função estimada para o período completo é comparada com aquelas estimadas para os sub-periodos de inflação alta e moderada, para verificar a estabilidade da formulação adotada. Conclui-se que se pode rejeitar a hipótese de que ela é estável. O modelo de Cagan é generalizado aqui em outra dimensão, considerando mecanismos alternativos de formação de expectativas, que podem ser adaptativas, como no modelo original, ou racionais. A hipótese de que expectativas adaptativas sejam racionais é também considerada. Conclui-se que a imposição da condição de racionalidade ao modelo com expectativas adaptativas não produz alterações importantes nos valores estimados.

辽北农田土壤农药残留特征及其对农产品安全影响

农药对产地环境，特别是对土壤的广泛污染严重威胁农产品安全和人类健康。因此，本文采用建立的除草剂和有机氯农药（OCPs）残留分析方法，开展了辽北地区土壤农药残留特征、阿特拉津和乙草胺田间消解动力学、土壤农药残留对农产品安全影响等方面研究。主要研究结果如下： 1. 分别建立了土壤、大米、蔬菜、玉米中3种除草剂和8种OCPs多残留分析方法。方法检出限介于0.04~1.30 ng•g-1之间；11种农药在0.01 (0.02)~1.0 (2.0) mg•L-1范围内线性良好，相关系数介于0.9963-0.9998之间；平均回收率介于71%-117%之间、相对标准偏差小于14.4%。 2. 阿特拉津和乙草胺在辽北农田土壤普遍残留；丁草胺、六氯苯、狄氏剂和艾氏剂在部分土壤有残留；乙草胺和丁草胺相对其它农药残留较高；阿特拉津、六氯苯、狄氏剂和艾氏剂残留量与相关报道和标准相比较低。除艾氏剂外，检出农药残留量经Box-Cox变换后，均服从正态分布。阿特拉津、乙草胺、丁草胺、六氯苯在不同土壤利用类型之间存在显著差异（P<0.05）。 3. 玉米地土壤中阿特拉津和乙草胺消解动态符合一级反应动力学模式，阿特拉津消解半衰期在12.2~59.8d之间，乙草胺在18.5~54.6d之间。喷施地阿特拉津和乙草胺消解速率约为对照地的2~5倍，且喷施量越大，消解越快。 4. 11种农药在辽北蔬菜、大米、玉米中残留较低，仅阿特拉津、六氯苯、乙草胺和丁草胺在部分农产品中有残留，其在土壤中残留通过蔬菜、大米和玉米给消费者带来的总膳食风险较低。大田试验进一步说明在试验区域喷施4倍最大推荐剂量阿特拉津或乙草胺也不会对玉米安全产生影响。

The Double Pareto-Lognormal Distribution and its applications in actuarial science and finance

Le but de ce mémoire de maîtrise est de décrire les propriétés de la loi double Pareto-lognormale, de montrer comment on peut introduire des variables explicatives dans le modèle et de présenter son large potentiel d'applications dans le domaine de la science actuarielle et de la finance. Tout d'abord, nous donnons la définition de la loi double Pareto-lognormale et présentons certaines de ses propriétés basées sur les travaux de Reed et Jorgensen (2004). Les paramètres peuvent être estimés en utilisant la méthode des moments ou le maximum de vraisemblance. Ensuite, nous ajoutons une variable explicative à notre modèle. La procédure d'estimation des paramètres de ce mo-\\dèle est également discutée. Troisièmement, des applications numériques de notre modèle sont illustrées et quelques tests statistiques utiles sont effectués.

Modified radial basis function neural network using output transformation

A modified radial basis function (RBF) neural network and its identification algorithm based on observational data with heterogeneous noise are introduced. The transformed system output of Box-Cox is represented by the RBF neural network. To identify the model from observational data, the singular value decomposition of the full regression matrix consisting of basis functions formed by system input data is initially carried out and a new fast identification method is then developed using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator (MLE) for a model base spanned by the largest eigenvectors. Finally, the Box-Cox transformation-based RBF neural network, with good generalisation and sparsity, is identified based on the derived optimal Box-Cox transformation and an orthogonal forward regression algorithm using a pseudo-PRESS statistic to select a sparse RBF model with good generalisation. The proposed algorithm and its efficacy are demonstrated with numerical examples.

Transformed symmetric models

For the first time, we introduce a class of transformed symmetric models to extend the Box and Cox models to more general symmetric models. The new class of models includes all symmetric continuous distributions with a possible non-linear structure for the mean and enables the fitting of a wide range of models to several data types. The proposed methods offer more flexible alternatives to Box-Cox or other existing procedures. We derive a very simple iterative process for fitting these models by maximum likelihood, whereas a direct unconditional maximization would be more difficult. We give simple formulae to estimate the parameter that indexes the transformation of the response variable and the moments of the original dependent variable which generalize previous published results. We discuss inference on the model parameters. The usefulness of the new class of models is illustrated in one application to a real dataset.

Genetic heterogeneity of within-family variance of body weight in Atlantic salmon (Salmo salar)

BACKGROUND: Canalization is defined as the stability of a genotype against minor variations in both environment and genetics. Genetic variation in degree of canalization causes heterogeneity of within-family variance. The aims of this study are twofold: (1) quantify genetic heterogeneity of (within-family) residual variance in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects. RESULTS: Analysis of body weight in Atlantic salmon using a double hierarchical generalized linear model (DHGLM) revealed substantial heterogeneity of within-family variance. The 95% prediction interval for within-family variance ranged from ~0.4 to 1.2 kg2, implying that the within-family variance of the most extreme high families is expected to be approximately three times larger than the extreme low families. For cross-sectional data, DHGLM with an animal mean sub-model resulted in severe bias, while a corresponding sire-dam model was appropriate. Heterogeneity of variance was not sensitive to Box-Cox transformations of phenotypes, which implies that heterogeneity of variance exists beyond what would be expected from simple scaling effects. CONCLUSIONS: Substantial heterogeneity of within-family variance was found for body weight in Atlantic salmon. A tendency towards higher variance with higher means (scaling effects) was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. For cross-sectional data, using the animal mean sub-model in the DHGLM resulted in biased estimates of variance components, which differed substantially both from a standard linear mean animal model and a sire-dam DHGLM model. Although genetic differences in canalization were observed, selection for increased canalization is difficult, because there is limited individual information for the variance sub-model, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes (diet, climatic region, etc.) may make genetic heterogeneity of variance a less stable trait over time and space.

A family of autoregressive conditional duration models

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box-Cox transformation with shape parameter λ to the conditional duration process and a possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power λ of the duration process. Finally, we assess the practical usefulness of our family of ACD models using NYSE transactions data, with special attention to IBM price durations. The results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks.

Testing production functions used in empirical growth studies

We estimate and test two alternative functional forms, which have been used in the growth literature, representing the aggregate production function for a panel of countries: the model of Mankiw, Romer and Weil (Quarterly Journal of Economics, 1992), and a mincerian formulation of schooling-returns to skills. Estimation is performed using instrumental-variable techniques, and both functional forms are confronted using a Box-Cox test, since human capital inputs enter in levels in the mincerian specification and in logs in the extended neoclassical growth model.