On Improvement in Estimating Population Parameter(s) Using Auxiliary Information

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers. The following problems have been discussed in the book: In chapter one an estimator in systematic sampling using auxiliary information is studied in the presence of non-response. In second chapter some improved estimators are suggested using auxiliary information. In third chapter some improved ratio-type estimators are suggested and their properties are studied under second order of approximation. In chapter four and five some estimators are proposed for estimating unknown population parameter(s) and their properties are studied. This book will be helpful for the researchers and students who are working in the field of finite population estimation.Comment: 63 pages, 8 tables. Educational Publishing & Journal of Matter Regularity (Beijing

A Branch and Bound Approach to Optimal Allocation in Stratified Sampling

For practical applications of any allocations, integer values of the sample sizes are required. This could be done by simply rounding off the non-integer sample sizes to the nearest integral values. When the sample sizes are large enough or the measurement cost in various strata are not too high, the rounded off sample allocation may work well. However for small samples in some situations the rounding off allocations may become infeasible and non-optimal. This means that rounded off values may violate some of the constraints of the problem or there may exist other sets of integer sample allocations with a lesser value of the objective function. In such situations we have to use some integer programming technique to obtain an optimum integer solution. Keywords:  Stratified sampling, Non-linear Integer Programming, Allocation Problem,  Langrangian Multiplier, Branch & Bound Techniqu

An Exponential Ratio Type Estimator of the Population Mean in The Presence of Non-Response Using Double Sampling

In modern era, proper and effective planning can be only possible using statistical techniques to estimate different characteristics of population under studies. An appropriate sample design based on efficient estimation technique is desirable to extract maximum information from sample data. It is a well-known phenomenon to use auxiliary information and to reduce the negative impact of non-response using Hansen & Hurwitz approach that further increase the efficiency of an estimator. Information on one or more auxiliary variables correlated with study variable in several ways to get more reliable estimate. The current paper presents a novel Exponential ratio type estimator to estimate the population mean under the problem of non- response. The proposed estimator further reduces the mean square error in the case of double sampling scheme. Approximate algebraic expressions of the mean square error are discussed; in addition, two real applications are also presented. Several ratio and regression type estimators were developed which perform better with several optimization constants under double sampling in the presence of non-response. However, the proposed estimator has utilized information on auxiliary variables in exponential form and place optimization constants in such positions which further increase the efficiency of the estimator even in all level of correlation coefficients among study and auxiliary variables. Real world data examples, as well as simulation study have been performed to know efficiency of the proposed method over mentioned competitors

Matching on-the-fly in Sequential Experiments for Higher Power and Efficiency

We propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in sequential randomized trials. Subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment. We develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test. Simulations illustrate the method's higher efficiency and power over competing allocation procedures in both controlled scenarios and historical experimental data.Comment: 20 pages, 1 algorithm, 2 figures, 8 table

The theory of multiple measurements techniques in distributed parameter systems

A comprehensive theory of multiple measurements for the optimum on-line state estimation and parameter identification in a class of noisy, dynamic distributed systems, is developed in this study. Often in practical monitoring and control problems, accurate measurements of a critical variable are not available in a desired form or at a desired sampling rate. Rather, noisy independent measurements of related forms of the variable may be available at different sampling rates. Multiple measurements theory thus involves the optimum weighting and combination of different types of available measurements. One of the contributions of this work is the development of a unique measurement projection method by which off-line measurements may be optimally utilized for on-line estimation and control. The analysis of distributed systems often requires the establishment of monitoring stations. Another contribution of this study is the development of a measurement strategy, based on statistical experimental design techniques, for the optimum spatial monitoring stations in a class of distributed systems. By incorporating in the optimization criterion, terms representing the realistic costs of making observations, an algorithm is developed for an estimator indicator whose values dictate an observation strategy for the optimum number and temporal intervals of observations. This, along with the optimum measurement stations thus provides a comprehensive monitoring policy on which the estimation and control of a distributed system may be based. By employing the measurement projection scheme and the monitoring policy, algorithms are further developed for Kalmantype distributed filters for the estimation of the state profiles based on all available on-line and off-line measurements. In the interest of a realistic engineering application, the developments in this study are based on a specific class of distributed systems representable by the mass transport models in environmental pollution systems. However, the techniques developed are equally applicable to a broader class of systems, including process control, where measurements may be characterized by noisy on-line instrumentation and off-line empirical laboratory tests. Although pertinent field data were not available for the research, the multiple measurements techniques developed were applied to several simulated numerical examples that do represent typical engineering problems. The results obtained demonstrate the consistent superiority of the techniques over existing estimation methods. Methods by which the results of this work may be integrated into real engineering problems are also discussed

Chapter Five. Systematic review results by biomarker classifications

5.1 Markers of Absorption and Permeability Overview 5.2 Markers of Absorption 5.3 Markers of Permeability 5.4 Markers of Digestion 5.5 Markers of Intestinal Inflammation and Intestinal Immune Activation 5.6 Markers of Systemic Inflammation and Systemic Immune Activation 5.7 Markers of Microbial Drivers 5.8 Markers of Nonspecific Intestinal Injury 5.9 Markers of Extra-Small Intestinal Function 5.10 Relationships Between Markers of EED, Including Histopathology 5.11 Relationships between EED Biomarkers and Growth or Other Outcomes of Interesthttps://digitalcommons.wustl.edu/tropicalenteropathybook/1006/thumbnail.jp

Solving optimisation problems in metal forming using FEM: A metamodel based optimisation algorithm

During the last decades, Finite Element (FEM) simulations of metal forming processes have\ud become important tools for designing feasible production processes. In more recent years,\ud several authors recognised the potential of coupling FEM simulations to mathematical opti-\ud misation algorithms to design optimal metal forming processes instead of only feasible ones.\ud This report describes the selection, development and implementation of an optimisa-\ud tion algorithm for solving optimisation problems for metal forming processes using time\ud consuming FEM simulations. A Sequential Approximate Optimisation algorithm is pro-\ud posed, which incorporates metamodelling techniques and sequential improvement strate-\ud gies for enhancing the e±ciency of the algorithm. The algorithm has been implemented in\ud MATLABr and can be used in combination with any Finite Element code for simulating\ud metal forming processes.\ud The good applicability of the proposed optimisation algorithm within the ¯eld of metal\ud forming has been demonstrated by applying it to optimise the internal pressure and ax-\ud ial feeding load paths for manufacturing a simple hydroformed product. Resulting was\ud a constantly distributed wall thickness throughout the ¯nal product. Subsequently, the\ud algorithm was compared to other optimisation algorithms for optimising metal forming\ud by applying it to two more complicated forging examples. In both cases, the geometry of\ud the preform was optimised. For one forging application, the algorithm managed to solve\ud a folding defect. For the other application both the folding susceptibility and the energy\ud consumption required for forging the part were reduced by 10% w.r.t. the forging process\ud proposed by the forging company. The algorithm proposed in this report yielded better\ud results than the optimisation algorithms it was compared to

Randomizing a clinical trial in neuro-degenerative disease

The paper studies randomization rules for a sequential two-treatment, two-site clinical trial in Parkinson’s disease. An important feature is that we have values of responses and five potential prognostic factors from a sample of 144 patients similar to those to be enrolled in the trial. Analysis of this sample provides a model for trial analysis. The comparison of allocation rules is made by simulation yielding measures of loss due to imbalance and of potential bias. A major novelty of the paper is the use of this sample, via a two-stage algorithm, to provide an empirical distribution of covariates for the simulation; sampling of a correlated multivariate normal distribution is followed by transformation to variables following the empirical marginal distributions. Six allocation rules are evaluated. The paper concludes with some comments on general aspects of the evaluation of such rules and provides a recommendation for two allocation rules, one for each site, depending on the target number of patients to be enrolled

Mean estimation of sensitive variables under measurement errors and non-response

This study mainly consists of three important issues we face in survey sampling: social desirability bias, measurement errors, and non-response. In this dissertation, we study the mean estimation of a sensitive variable under measurement errors and non-response. We propose a generalized mean estimator, then discuss the bias and the mean square error (MSE) of this estimator and present the comparisons with other estimators under the measurement errors and non-response using optional RRT model (ORRT). We also study the performance of the proposed estimator under the same situations using stratified random sampling. Simulation studies are also conducted to verify the theoretical results. Both the theoretical and empirical results show that the generalized mean estimator is more efficient than the ordinary RRT estimator that does not utilize the auxiliary variable, and the ratio estimator which is one of the commonly used mean estimator