A note about calibrated prediction regions and distributions

In this work we address the problem of the construction of prediction regions and distribution functions, with particular regard to the multidimensional setting. Firstly, we define a simple procedure for calculating the predictive distribution function which gives improved prediction limits. Secondly, with a multivariate generalization of a result presented in Ueki and Fueda (2007), we propose a method for correcting estimative prediction regions, to reduce their coverage error to the third-order accuracy. The improved prediction regions and the associated distribution functions are easy to calculate using a suitable bootstrap procedure. Examples of application are included, showing the good performance of the proposed method, even if we consider an approximated model for prediction purposes.     

Decomposable pseudodistances and applications in statistical estimation

The aim of this paper is to introduce new statistical criteria for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools imbedding the most classical ones, such as maximum likelihood, Chi-square or Kullback–Leibler. General pseudodistances with decomposable structure are considered, they allowing defining minimum pseudodistance estimators, without using nonparametric density estimators. A special class of pseudodistances indexed by α>0$\alpha >0$, leading for α↓0$\alpha \downarrow 0$ to the Kullback–Leibler divergence, is presented in detail. Corresponding estimation criteria are developed and asymptotic properties are studied. The estimation method is then extended to regression models. Finally, some examples based on Monte Carlo simulations are discussed.     

Standardization of Process Norms in Baker's Yeast Fermentation through Statistical Models in Comparison with Neural Networks

Achieving consistency of growth pattern for commercial yeast fermentation over batches through addition of water, molasses and other chemicals is often very complex in nature due to its bio-chemical reactions in operation. Regression models in statistical methods play a very important role in modeling the underlying mechanism, provided it is known. On the contrary, artificial neural networks provide a wide class of general-purpose, flexible non-linear architectures to explain any complex industrial processes. In this paper, an attempt has been made to find a robust control system for a time varying yeast fermentation process through statistical means, and in comparison to non-parametric neural network techniques. The data used in this context are obtained from an industry producing baker's yeast through a fed-batch fermentation process. The model accuracy for predicting the growth pattern of commercial yeast, when compared among the various techniques used, reveals the best performance capability with the backpropagation neural network. The statistical model used through projection pursuit regression also shows higher prediction accuracy. The models, thus developed, would also help to find an optimum combination of parameters for minimizing the variability of yeast production.     

A Cautionary Note on Beta Families of Distributions and the Aliases Within

In this note, we examine the four parameter beta family of distributions in the context of the beta-normal and beta-logistic distributions. In the process, we highlight the concept of numerical and limiting alias distributions, which in turn relate to numerical instabilities in the numerical maximum likelihood fitting routines for these families of distributions. We conjecture that the numerical issues pertaining to fitting these multiparameter distributions may be more widespread than has originally been reported across several families of distributions.     

On evaluating the performance of different forecasters

In this article, we have evaluated the performance of different forecasters and tested association between their performances for different pairs of variables. We have used three data sets of track records of professional U.S. economic forecasters participating in the Blue Chip consensus forecasting service (the data sets contain the root mean square errors (RMSE) of different forecasters for different years). To evaluate the performance of forecasters we have covered three well-known tests, namely the usual F test (cf. Fisher (1923 Fisher, R. A., Mackenzie, M. A. (1923). Studied in crop variation II. The manurial response of different potato. Journal of Agricultural Science 13:311–320. [Google Scholar])), Kruskal Wallis test (cf. Kruskal and Wallis (1952 Kruskall, W. H., Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of American Statistical Association 47:583–621. [Google Scholar])), and Extension of Median test (cf. Daniel (1990 Daniel, W. W. (1990). Applied Nonparametric Statistics. Duxbury Classic Series. (2nd Ed.), Boston. [Google Scholar])). To test the association between the forecaster's performances for different pairs of variables, we have considered Gini mean correlation coefficient r_g1 (cf. Yitzhaki, S., and Olkin, I. (1991 Yitzhaki, S., Olkin, I. (1991). Concentration indices and concentration curves, in K. Mosler and M. Scarsini (eds.), Stochastic Orders and Decisions under Risk, Institute of Mathematical Statistics: Lecture-Notes Monograph Series, 19, 1991, 380–392. [Google Scholar]) and Yitzhaki (2003 Yitzaki, S. (2003). Gini mean difference: A superior measure of variability for non normal distribution. Metron-International Journal of Statistics, LXI:285–316. [Google Scholar])), Modified rank correlation coefficient (cf. Zimmerman (1994 Zimmerman, D. W. (1994). A Note on modified rank correlation. Journal of educational and Behavioral Statistics 19:357–362. [Google Scholar])) and three modifications of Spearman rank correlation coefficient. We have observed that different forecasters do not necessarily offer same average performance. Moreover, an evidence of association between two criteria does not always lead us reaching at the same decision. The outcomes of the study may help the practitioners in selecting the best forecaster(s) for policymaking purposes.     

Parametric bootstrap inferences for panel data models

This article presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation for the regression coefficients and the variance components of panel data regression models with complete panels. The PB pivot variables are proposed based on sufficient statistics of the parameters. On the other hand, we also derive generalized inferences and improved generalized inferences for variance components in this article. Some simulation results are presented to compare the performance of the PB approaches with the generalized inferences. Our studies show that the PB approaches perform satisfactorily for various sample sizes and parameter configurations, and the performance of PB approaches is mostly the same as that of generalized inferences with respect to the expected lengths and powers. The PB inferences have almost exact coverage probabilities and Type I error rates. Furthermore, the PB procedure can be simply carried out by a few simulation steps, and the derivation is easier to understand and to be extended to the incomplete panels. Finally, the proposed approaches are illustrated by using a real data example.     

Estimating Risk Assessment Exposure Point Concentrations when the Data Are Not Normal or Lognormal

The U.S. Environmental Protection Agency (EPA) recommends the use of the one-sided 95% upper confidence limit of the arithmetic mean based on either a normal or lognormal distribution for the contaminant (or exposure point) concentration term in the Superfund risk assessment process. When the data are not normal or lognormal this recommended approach may overestimate the exposure point concentration (EPC) and may lead to unecessary cleanup at a hazardous waste site. The EPA concentration term only seems to perform like alternative EPC methods when the data are well fit by a lognormal distribution. Several alternative methods for calculating the EPC are investigated and compared using soil data collected from three hazardous waste sites in Montana, Utah, and Colorado. For data sets that are well fit by a lognormal distribution, values for the Chebychev inequality or the EPA concentration term may be appropriate EPCs. For data sets where the soil concentration data are well fit by gamma distributions, Wong's method may be used for calculating EPCs. The studentized bootstrap-t and Hall's bootstrap-t transformation are recommended for EPC calculation when all distribution fits are poor. If a data set is well fit by a distribution, parametric bootstrap may provide a suitable EPC.     

Optimal Tests for No Contamination in Reliability Models

Inferences on mixtures of probability distributions, in general,and of life distributions, in particular, are receiving considerableimportance in recent years. The likelihood ratio procedure oftesting for the null hypothesis of no contamination is oftenvery cumbersome and lacks its usual asymptotic properties. Recently,SenGupta (1991) has introduced the notion of an `L-optimal' testfor such testing problems. The idea is to recast the originalseveral parametric hypotheses representation of the null hypothesisin terms of only a single hypothesis involving an appropriatelychosen parametric function. This approach is shown to be bothmathematically elegant and operationally simple for a quite generalclass of mixture distributions which contains, in particular,all mixtures of the one-parameter exponential family and alsoa very rich subclass of mixtures useful in life-testing and reliabilityanalysis. It is also illustrated through two examples—onebased on real-life data and the other on a simulated sample.     

Parametric Design in Urbanism: A Critical Reflection

Parametric modelling run by the explicitly defined algorithms generating synchronically auditable dynamic forms and patterns, has become a prominent method especially in architecture. Though the use of parametric models has got wider in urban design, the critical reflection on the actual and possible application of the method in urbanism has fallen limited so far. The paper tends to relate parametric design with the contemporary understanding of urbanism with regards to the idea of design control in the the context of complexity. From this perspective, the actual performance of the model application in urban context is discussed with the renowned project of Kartal-Pendik Masterplan (Zaha Hadid Architects) in Istanbul, Turkey.     

On Charlier polynomials in testing Poissonity

This article discusses applications of Charlier polynomials when checking how well classic Poisson model fits the data. We show that smooth components pertaining to the polynomials can be effectively used in preliminary analysis of data at hand and we propose and discuss some tests based on them. Our extensive simulations shed new light on power behavior of the best tests in the area.