Numerical algorithms for solving nonlinear L р-norm estimation problems: part II - a mixture method for large residual and illo-conditioned problems

The nonlinear least squares algorithm of Gill and Murray (1978) is extended and modified to solve nonlinear L _р-norm estimation problems efficiently. The new algorithm uses a mixture of 1st-order derivative (Guass-Newton) and 2nd-order derivative (Newton) search directions. A new rule for selecting the “grade” r of the p-jacobiab matrix J_p was also incorporated. This brought about rapid convergence of the algorithm on previously reported test examples.     

Humps and Bumps in Lifetime Consumption

In this article we argue that the life-cycle model that allows demographics to affect household preferences and relaxes the assumption of certainty equivalence can generate hump-shaped consumption profiles over age that are very similar to those observed in household-level data sources and, in particular, match the differences in shape across different education groups. Liquidity constraints or myopia are not required to explain the empirical features of observed life-cycle patterns.     

Comparative Study of Predictive Computational Models for Nanoparticle‐Induced Cytotoxicity

With the increasing use of nanomaterials incorporated into consumer products, there is a need for developing approaches to establish “quantitative structure‐activity relationships” (QSARs). These relationships could be used to predict various biological responses after exposure to nanomaterials for the purposes of risk analysis. This risk analysis is applicable to manufacturers of nanomaterials in an effort to determine potential hazards. Because metal oxide materials are some of the most widely applicable and studied nanoparticle types for incorporation into cosmetics, food packaging, and paints and coatings, we focused on comparing different approaches for establishing QSARs for this class of materials. Metal oxide nanoparticles are believed, by some, to cause alterations in cellular function due to their size and/or surface area. Others have said that these nanomaterials, because of the oxidized state of the metal, do not induce stress in biological tests systems. This controversy highlights the need to systematically develop structure‐activity relationships (i.e., the relationship between physicochemical features to the cellular responses) and tools for predicting potential biological effects after a metal oxide nanomaterial exposure. Here, we attempt to identify a set of properties of two specific metal oxide nanomaterials—TiO₂ and ZnO—that could be used to characterize and predict the induced cellular membrane damage of immortalized human lung epithelial cells. We adopt a mathematical modeling approach that uses the engineered nanomaterial size characterized as a dry nanopowder and the nanomaterial behavior in ultrapure water, phosphate buffer, and cell culture media to predict nanomaterial‐induced cellular membrane damage (via lactate dehydrogenase release). Results of these studies provide insights on how engineered nanomaterial features influence cellular responses and thereby outline possible approaches for developing and applying predictive computational models for biological responses caused by exposure to nanomaterials.     

Prediction under uncertainty of degree of polynomial in growth curve models

Random coefficient polynomial regression model has been considered for prediction purpose when there is uncertainty about the degree of the polynomialo Expressions for mean square errors of two predictors based on simple estimators have been derived and their perfomaiices have been compared when parameters are estimated from the sample. A modified predictor has also been suggested when parameters in the predicting equations are to be estimated from the sample. Perform-ance ofseveral predictors haife been compared by cross validation technique from a real set of data.     

A bound connected with 26 factorial search designs of resolution 3.1

In this paper, we give a lower bound for the number of treatments required

for a plan to be a main effect plus one plan for 2^m (m = 6) factorial experiments, The lower bound problem is important in the event of generating new designs with similar properties or when one wants to study the criteria of optimality for such designs.     

Bayesian Approach to Multicentre Sparse Data

In a 2 × 2 contingency table, when the sample size is small, there may be a number of cells that contain few or no observations, usually referred to as sparse data. In such cases, a common recommendation in the conventional frequentist methods is adding a small constant to every cell of the observed table to find the estimates of the unknown parameters. However, this approach is based on asymptotic properties of the estimates and may work poorly for small samples. An alternative approach would be to use Bayesian methods in order to provide better insight into the problem of sparse data coupled with fewer centers, which would otherwise be difficult to carry out the analysis. In this article, an attempt has been made to use hierarchical Bayesian model to a multicenter data on the effect of a surgical treatment with standard foot care among leprosy patients with posterior tibial nerve damage which is summarized as seven 2 × 2 tables. Monte Carlo Markov Chain (MCMC) techniques are applied in estimating the parameters of interest under sparse data setup.     

A Benchmarking Approach to Forecast Combination

This article is concerned with the development of a statistical model-based approach to optimally combine forecasts derived from an extrapolative model, such as an autoregressive integrated moving average (ARIMA) time series model, with forecasts of a particular characteristic of the same series obtained from independent sources. The methods derived combine the strengths of all forecasting approaches considered in the combination scheme. The implications of the general theory are investigated in the context of some commonly encountered seasonal ARIMA models. An empirical example to illustrate the method is included.     

Estimability,testability, and connectedness in the cell means model

This article discusses the conocepts of estimation of parameters and tests of linear hyp hypotheses in the fixed effects (ANOVA) model with some zero cell frequencies. The concept of connected experiments is generalized ot he cel1-means model and relatedtotheest imation of and test of hy pothe sesa bout the cell means. A simple test for connectedness is developed as a n atur alre sult of thea nalysis of the constrai nedcell means model. The a nalysis of unconnected experimentsisbriefly discussed. Examples are presented toillustrate the ideas.     

Statistical Reversion toward the Mean: More Universal than Regression toward the Mean

Schmittlein discussed the lack of universality of regression toward the mean. The present note emphasizes the universality of a similar effect, dubbed “reversion” toward the mean, defined as the shift in conditional expectation of the upper or lower portion of a distribution. Reversion toward the mean is a useful concept for statistical reasoning in applications and is more self-evidently plausible than regression toward the mean.     

Comparing alternating logistic regressions to other approaches to modelling correlated binary data

Alternating logistic regressions (ALRs) seem to offer some of the advantages of marginal models estimated via generalized estimating equations (GEE) and generalized linear mixed models (GLMMs). Via simulation study we compared ALRs to marginal models estimated via GEE and subject-specific models estimated via GLMMs, with a focus on estimation of the correlation structure in three-level data sets (e.g. students in classes in schools). Data set size and structure, and amount of correlation in the data sets were varied. For simple correlation structures, ALRs performed well. For three-level correlation structures, all approaches, but especially ALRs, had difficulty assigning the correlation to the correct level, though sample sizes used were small. In addition, ALRs and GEEs had trouble attaching correct inference to the mean effects, though this improved as overall sample size improved. ALRs are a valuable addition to the data analyst's toolkit, though care should be taken when modelling data with three-level structures.