This thesis discusses various issues in the estimation of models for count data. In the first part of the thesis, we derive an analytic expression for the bias of the maximum likelihood estimator (MLE) of the parameter in a doubly-truncated Poisson distribution, which proves highly effective as a means of bias correction. We explore the circumstances under which bias is likely to be problematic, and provide some indication of the statistical significance of the bias. Over a range of sample sizes, our method outperforms the alternative of bias correction via the parametric bootstrap. We show that MLEs obtained from sample sizes which elicit appreciable bias also have sampling distributions which are unsuited to be approximated by large-sample asymptotics, and bootstrapping confidence intervals around our bias-adjusted estimator is preferred, as two tiers of bootstrapping may incur a heavy computational burden. Modelling count data where the counts are strictly positive is often accomplished using a positive Poisson distribution. Inspection of the data sometimes reveals an excess of ones, analogous to zero-inflation in a regular Poisson model. The latter situation has well developed methods for modelling and testing, such as the zero-inflated Poisson (ZIP) model, and a score test for zero-inflation in a ZIP model. The issue of count inflation in a positive Poisson distribution does not seem to have been considered in a similar way. In the second part of the thesis, we propose a one-inflated positive Poisson (OIPP) model, and develop a score test to determine whether there are “too many” ones for a positive Poisson model to fit well. We explore the performance of our score test, and compare it to a likelihood ratio test, via Monte Carlo simulation. We find that the score test performs well, and that the OIPP model may be useful in many cases. The third part of the thesis considers the possibility of one-inflation in zero-truncated data, when overdispersion is present. We propose a new model to deal with such a phenomenon, the one-inflated zero-truncated negative binomial (OIZTNB) model. The finite sample properties of the maximum likelihood estimators for the parameters of such a model are discussed. This Chapter considers likelihood ratio tests which assist in specifying the OIZTNB model, and investigates the finite sample properties of such tests. The OIZTNB model is illustrated using the medpar data set, which describes the hospital length of stay for a set of patients in Arizona. This is a data set that is widely used to highlight the merits of the zero-truncated negative binomial (ZTNB) model. We find that our OIZTNB model fits the data better than does the ZTNB model, and this leads us to conclude that the data are generated by a one-inflated process. / Graduate

No description available.

Thesis (doctoral)--Bayerische Ludwig Maximilians Universität, Munich, 1933.

Thesis (doctoral)--Bayerische Ludwig Maximilians Universität, Munich, 1933.

No description available.

Diss. (sammanfattning) Stockholm : Karol. inst., 2001. / Härtill 5 uppsatser.

Several standard methods are available to analyze and estimate parameters of count data. None of these methods are designed to account for potential misclassification of the data, where counts are observed or recorded as higher or lower than their actual value. These false counts can result in erroneous conclusions and biased estimates. For this paper, a standard estimation model was modified in several ways in order to incorporate each misclassification mechanism. The probability distribution of the observed data was derived and combined with informative distributions for the misclassification parameters. Once this additional information was taken into account, a distribution of observed data conditional on only the parameter of interest was obtained. By incorporating information about the misclassification mechanisms, the resulting estimation will be more accurate than the standard methods. To demonstrate the flexibility of this approach, data from a count distribution affected by various misclassification mechanisms were simulated. Each dataset was analyzed by several standard estimation methods and an appropriate new method. The results from all simulated data were compared, and the impact of each mechanism in regards to each estimation method was discussed. Data from a colorectal polyp prevention study were also analyzed with all available methods to showcase the incorporation of additional covariates.

Indiana University-Purdue University Indianapolis (IUPUI) / There are two computational bottlenecks for Big Data analysis: (1) the data is too large for a desktop to store, and (2) the computing task takes too long waiting time to finish. While the Divide-and-Conquer approach easily breaks the first bottleneck, the Subsampling approach simultaneously beat both of them. The uniform sampling and the nonuniform sampling--the Leverage Scores sampling-- are frequently used in the recent development of fast randomized algorithms. However, both approaches, as Peng and Tan (2018) have demonstrated, are not effective in extracting important information from data. In this thesis, we conduct regression analysis for big count data via A-optimal subsampling. We derive A-optimal sampling distributions by minimizing the trace of certain dispersion matrices in general estimating equations (GEE). We point out that the A-optimal distributions have the same running times as the full data M-estimator. To fast compute the distributions, we propose the A-optimal Scoring Algorithm, which is implementable by parallel computing and sequentially updatable for stream data, and has faster running time than that of the full data M-estimator. We present asymptotic normality for the estimates in GEE's and in generalized count regression. A data truncation method is introduced. We conduct extensive simulations to evaluate the numerical performance of the proposed sampling distributions. We apply the proposed A-optimal subsampling method to analyze two real count data sets, the Bike Sharing data and the Blog Feedback data. Our results in both simulations and real data sets indicated that the A-optimal distributions substantially outperformed the uniform distribution, and have faster running times than the full data M-estimators.

Fifty-eight meat and poultry plants in Virginia were assessed during spring and summer of 2000. These assessments were all conducted in the presence of state inspection and were designed to be non-regulatory. The audit team included N.G. Marriott, M.A. Tolbert and B.P. Quinn. The audits consisted of a tour of the facility and a review of SSOPs and all HACCP related documentation. To assist in these audits, a HACCP check sheet was developed and utilized to indicate suggestions or deficiencies. Most of the plants had an understanding of how to implement HACCP properly. The majority of the suggestions that were noted were not so much about the HACCP concept, but more with regards to the legality of a HACCP document. The most noted deficiency was improper cross-outs. If there is a correction, one line should be drawn through the error and then must be initialed. With respect to the HACCP plan, most deficiencies were related to the hazards and the critical control points. During these audits, two microbial determination methods (Standard Plate Count and Bioluminescence) were used to evaluate processing equipment. Typically, three pieces of equipment were tested at each plant. When the data were collected, the two microbial determination methods were correlated. The "corr" function in SAS resulted in a correlation coefficient of .4478, which is low and indicates a poor correlation. A pass/fail method similar to one done by Illsley et. al. resulted in a 48.9% agreement between the methods in this research. / Master of Science

Doctor of Philosophy / Department of Food Science / Daniel Y.C. Fung / In the food industry, coliform testing is traditionally done by the time consuming and labor intensive plate count method or tube enumeration methods. The TEMPO® system (bioMérieux, Inc.) was developed to improve laboratory efficiency and to replace traditional methods. It uses a miniaturization of the Most Probable Number (MPN) method with 16 tubes with 3 dilutions in one single disposable card. It utilizes two stations: the TEMPO® Preparation station and the TEMPO® Reading station. In this study, the Oxyase® (Oxyase®, Inc.) enzyme was added to TEMPO® CC (Coliforms Count), TEMPO® AC (aerobic colony count) and TEMPO® EC (E. coli Count) methods. Water samples of 1 ml with 0.1 ml of Oxyase® enzyme were compared to samples without the Oxyase® enzyme using the TEMPO® system. Samples were spiked with different levels of coliforms (10, 102, 103 and 104 CFU/ml), stomached (20 sec), and pipetted into the three different TEMPO® media reagents (4 ml) in duplicate and then automatically transferred into the corresponding TEMPO® cards by the TEMPO® preparation station. Counts were obtained using the TEMPO® reading station after 8, 12, 16, 22 and 24 hours at an incubation temperature of 35°C. Results from 20 replicates were compared statistically. Using TEMPO® tests, high counts in food samples (>6 log 10 CFU/ml) can be read in 6±2 hours of incubation using the time-to-detection calibration curve. The TEMPO® system reduces reading time (reading protocol should be changed). There is no need to wait for 22 hours of incubation only 12 hours is required. Oxyrase® enzyme is not needed for the TEMPO® system.