Accounting for uncertainty in control-relevant statistics

Using given significant additional information it is possible to improve different confidence regions for the regression parameters in a linear model. Thereby, the given informations may concern the expectation and (or) the variance of the observations, and an improvement is possible in the sense of the decrease of the confidence regions' size. In particular it is possible to improve the so called confidence ellipsoids which are often used to estimate the considered parameters.

Construction of confidence intervals or regions is an important part of statistical inference. The usual approach to constructing a confidence interval for a single parameter or confidence region for two or more parameters requires that the distribution of estimated parameters is known or can be assumed. In reality, the sampling distributions of parameters of biological importance are often unknown or difficult to be characterized. Distribution-free nonparametric resampling methods such as bootstrapping and permutation have been widely used to construct the confidence interval for a single parameter. There are also several parametric (ellipse) and nonparametric (convex hull peeling, bagplot and HPDregionplot) methods available for constructing confidence regions for two or more parameters. However, these methods have some key deficiencies including biased estimation of the true coverage rate, failure to account for the shape of the distribution inherent in the data and difficulty to implement. The purpose of this paper is to develop a new distribution-free method for constructing the confidence region that is based only on a few basic geometrical principles and accounts for the actual shape of the distribution inherent in the real data. The new method is implemented in an R package, distfree.cr/R. The statistical properties of the new method are evaluated and compared with those of the other methods through Monte Carlo simulation. Our new method outperforms the other methods regardless of whether the samples are taken from normal or non-normal bivariate distributions. In addition, the superiority of our method is consistent across different sample sizes and different levels of correlation between the two variables. We also analyze three biological data sets to illustrate the use of our new method for genomics and other biological researches.

In this paper we consider the problem of estimating confidence regions for the parameters of ARMA models. Based on subsampling techniques and building on earlier exact finite sample results due to Hartigan, we compute the exact probability that the true parameters belong to certain regions in the parameter space. By intersecting these regions, a confidence region containing the true parameters with guaranteed probability is then obtained. All results hold true for a finite number of data points and no asymptotic theory is used. The usefulness of the approach is illustrated in a simulation example.

Asymptotic properties of SPS confidence regions

[] Based on a single and on two independent samples, joint confidence regions for parameters of Pareto distributions are proposed with minimum volume properties and without assigning the confidence level to dimensions. In the one-sample case, comparisons are made to former simultaneous confidence sets for Pareto parameters by means of simulation and a real data set. The two-sample case is studied in various set-ups and comprises simultaneous confidence regions for the shape parameters, the scale parameters, and higher-dimensional vectors of these parameters, where common shape and common scale models are also considered.

This study aimed to evaluate the adaptability and phenotypic stability of cowpea genotypes using a nonlinear regression analysis and multivariate analysis. Experiments were performed at four sites in Brazil using a randomized blocks design with 20 treatments and four replications. The adaptability and stability of genotypes were evaluated by Toler nonlinear regression and genotype plus genotype × environment (GGE) biplot methodologies. Most of the genotypes revealed linear response patterns, with no differences regarding the favorable and unfavorable environments. Regarding the genotype classification for stability and adaptability, the Toler and GGE biplot methodologies are congruent. Genotypes MNC99-537F-4, MNC00-561G-6, MNC99542F-5, and Patativa have high overall adaptability and adequate yield. Therefore, they should be recommended for cultivation in the tested environments. Genotypes closer to the ideotype by the GGE biplot method are considered doubly desirable by the nonlinear method.

Empirical likelihood for single-index models

Robustness of confidence region for linear model parameters following a misspecified transformation of dependent variable is studied. It is shown that when error standard deviation is moderate to large the usual confidence region is robust against transformation misspecification. When error standard deviation is small the usual confidence region could be very conservative for structured models and slightly liberal for unstructured models. However, the conservativeness in structured case can be controlled if the transformation is selected with the help of data rather than prior information since this is the case when data is able to provide a very accurate estimate of transformation.

Mathematical separation of multi-component exponential signals from the u.v. laser excitation of glycogen phosphorylase [formula omitted

Modeling of resistance spot welding process on galvanized steel sheet was investigated. Mathematical models developed by nonlinear multiple regression analysis and artificial neural network approach were employed in the prediction of welding quality factors, namely nugget diameter, penetration rate and tensile shear strength, under some welding conditions. According to the prediction models on quality, the prediction systems of welding process parameters were formulated respectively on the basis of Newton-Raphson iterative algorithm and cascade forward back propagation algorithm in order to obtain the desired welding quality. The results showed that the prediction precision of cascade forward back propagation algorithm was higher than Newton-Raphson iterative algorithm. The current duration had the largest prediction error, followed by electrode force and welding current. Therefore, it was concluded that the current duration was the most difficult parameter in prediction system of welding process in order to obtain the desired welding quality.

In this investigation, point estimation, confidence regions, and testing statistical hypotheses for various functions of interest are considered. The inference is carried out for the survival function, hazard function and its derivatives, cumulative hazard function and the pth quantile. Different, but most commonly occurring, censoring and truncation schemes are chosen. Besides, useful central limit theory results and their rates of convergence, qualitative properties of the underlying estimators are discussed. Wherever possible the means and variances of the estimators are given. Some open problems are also briefly mentioned.

A jack knife procedure for constructing confidence regions in nonlinear regression is examined using Monte Carlo simulation. The jack knife promises to be asymptotically double-edged, being both independent of linearizing approximations to the regression surface and insensitive to specification of the error distribution. For moderate sample sizes the jack knife cannot be trusted in establishing joint confidence regions.

For a response surface experiment, an approximate hypothesis test and an associated confidence region is proposed for the minimizing (or maximizing) factor-level configuration. Carter et al. (1982, Cancer Research 42, 2963-2971) show that confidence regions for optimal conditions provide a way to make decisions about therapeutic synergism. The response surface may be constrained to be within a specified, bounded region. These constraint regions can be quite general. This allows for more realistic constraint modeling and a wide degree of applicability, including constraints occurring in mixture experiments. The usual assumption of a quadratic model is also generalized to include any regression model that is linear in the model parameters. An intimate connection is established between this confidence region and the Box-Hunter (1954, Biometrika 41, 190-199) confidence region for a stationary point. As a byproduct, this methodology also provides a way to construct a confidence interval for the difference between the optimal mean response and the mean response at a specified factor-level configuration. The application of this confidence region is illustrated with two examples. Extensive simulations indicate that this confidence region has good coverage properties.

Wiley-Interscience Paperback Series Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models ...highly recommend[ed] ...for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression -Technometrics [This book] provides a good balance of relevant theory and application with many examples ...[and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students. -Mathematical Reviews [This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition ...[and is] a worthwhile reference for the marketing researcher with a serious interest in linear models. -Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. book also includes pseudocode for computing algorithms.

In the context of two-wave with diffuse power (TWDP) fading scenarios, this paper analyzes the outage probability and symbol error rate (SER) of single relay cooperative networks using amplify-and-forward (AF) relaying. Each channel in the network is assumed to be independently and non-identically distributed. The statistical result of the upper bound on the received signal-to-noise ratio (SNR) is derived. We derive the closed-form asymptotic expressions to approximate the outage probability and SER in the high SNR regime, respectively. Based on the asymptotic results, the diversity order and coding gain of the cooperative network is analyzed. Simulation results show that these asymptotic results are tight particularly in the high SNR regime for cooperative networks in different fading scenarios.