SiZer for time series: A new approach to the analysis of trends

Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are `really there' and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish `trend' from `dependence'. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.Comment: Published at http://dx.doi.org/10.1214/07-EJS006 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modelling the kinetics of thermal inactivation of apple polyphenoloxidase

The enzymatic browning of fruits and vegetables caused by mechanical injury during postharvest storage or processing is initiated by the catalytic action of polyphenoloxidase (PPO). A bleaching treatment prior to processing is still considered mostly effective in inhibiting the catalytic activity of PPO, and thus controlling undesirable enzymatic browning. In this work, different mathematical routines were assessed in terms of their adequacy to describe the thermal inactivation of PPO from Golden apples over a range of temperatures from 62.5 to 72.5 ºC. The classical approach to kinetic modelling of the decay activity of apple PPO, commonly reported to follow a first-order model, employs a two-step procedure, in which the model parameters are individually obtained, by each temperature studied, using non-linear or linear regressions. Thereafter, the estimated parameters are further used to calculate their temperature dependence. Alternatively, a one-step method provides a regression fit to all experimental data sets, with the temperature dependence equation being directly built in the kinetic model. This fitting technique thus, (a) avoids the estimation of intermediate parameters and, (b) substantially increases the degrees of freedom and hence the precision of parameters’ estimates. Within this issue was further explored the logarithmic transformation of the mathematical equations used on the adequacy of the model to describe experimental data. In all cases non-weighted least-squares regression procedures were used. Both the examination and criticism of the current modelling strategies were done by assessing statistical data obtained, such as the confidence intervals of the estimates, correlation coefficients, sum of squares, and residuals normality

Scalable visualisation methods for modern Generalized Additive Models

In the last two decades the growth of computational resources has made it possible to handle Generalized Additive Models (GAMs) that formerly were too costly for serious applications. However, the growth in model complexity has not been matched by improved visualisations for model development and results presentation. Motivated by an industrial application in electricity load forecasting, we identify the areas where the lack of modern visualisation tools for GAMs is particularly severe, and we address the shortcomings of existing methods by proposing a set of visual tools that a) are fast enough for interactive use, b) exploit the additive structure of GAMs, c) scale to large data sets and d) can be used in conjunction with a wide range of response distributions. All the new visual methods proposed in this work are implemented by the mgcViz R package, which can be found on the Comprehensive R Archive Network

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.Comment: 21 pages, 3 figures, 5 tables. Computational Statistics and Data Analysis, 17 October 2011, ISSN 0167-9473 (http://www.sciencedirect.com/science/article/pii/S0167947311003628