Applications of statistical methods and techniques to auditing and accounting

Statistical Methods;Auditing;accounting/ accountancy

Statistical methods and applications to animal breeding

This thesis comprises a collection of 39 research papers divided into three groups. The first group discusses the development of statistical methods, especially novel methods of variance component estimation, with general application. The second group examines the potential use of statistical methods in animal breeding studies, ranging from the construction of new experimental designs to the analysis of non-normal data. The third group reports on studies on animal breeding data in beef and dairy cattle.Group I is entitled "Statistical methods, including variance component estimation, with general application". The major theme of this group is the estimation of variance components. Some previous work based on methods for balanced data, gave rise to methods that were neither unique nor efficient and other methods gave results that are inconsistent with the analysis of variance for balanced data. A method was introduced, now known as REML (Residual Maximum Likelihood) that unifies the area. The method was introduced for the analysis of incomplete block designs with unequal block size but was found to have important applications in the analysis of groups of similar trials, time-series and animal breeding. Papers investigating REML estimation for multivariate data, time-series and detecting outliers are included. The relationship of REML to other methods is elucidated, especially for balanced and partially balanced designs. Computational strategies are discussed.The last two papers in the group illustrate a method of analysis of dial lei crosses that involves using multiple copies of the data. This idea of using multiple copies was shown also to be useful in the analysis of rectangular lattice designs and in the interpretation of some recently introduced neighbour analyses of field trials.The next group of papers, Group II, report on "Application of statistical methods to animal breeding studies". The work on variance components has some application in animal breeding and I have built on these links. Four papers consider efficient designs for estimation of genetic parameters, including designs for estimating heritability from data on two generations of data, for estimating maternal genetic variances, for estimating parent-offspri ng regression and for estimating multivariate genetic parameters. These designs can lead to substantial reductions in the variances of the estimates of the parameters, compared with classical designs, halving variances in some cases. Other papers have shown how to efficiently estimate heritability from unbalanced data, both from two generations of data and from more than two generations.Often in animal breeding experiments animals used as parents are not selected at random, but selected on phenotypic measurements, perhaps of relatives. This can cause bias in some methods of estimation. On the other hand REML estimates can take account of the selection process. Selection experiments and the estimation of realised heritability are discussed.REML estimation has found widespread acceptance by animal breeders, partly because some quantities arising in the methods were terms that animal breeders use in evaluating animals. It was shown how to improve one method of evaluation and methods of evaluating sires were reviewedSome work is included on multivariate evaluation. It is shown how the complex multivariate calculations can be reduced to simpler univariate calculations using a canonical transformation, how results on selection indices can be used to interpret multivariate predictions. A simple interpretation of quadratic selection indices is given.Other work considered some parallel problems with non-normal data. In particular for binary data, estimation of heritability, optimal designs for estimation of heritability and prediction of breeding values. It was shown how to estimate genotype frequencies using generalised linear model methods and > h? suggested how to evaluate animals worth and estimate genetic parameters when the data fits a generalised linear model.The last group, Group III, is entitled "Experimental studies". These include reports on a long term study of evaluation of breeds and cross-breeding in beef cattle in Zambia. The section also examines the genetic relationship between meat and milk production in British Friesian cattle. The validity of models used in dairy sire evaluation are investigated including the heterogeneity of heritability of milk yield at different levels of production and the use of a novel model for taking account of environmental variation within herds.GROUP I: STATISTICAL METHODS INCLUDING VARIANCE COMPONENT ESTIMATE WITH GENERAL APPLICATION01. R. THOMPSON. 1969. Iterative estimation of variance components for non-orthogonal data. Biometrics 25, 767-773. || 02. H.D. PATTERSON and R. THOMPSON. 1971. Recovery of inter-block information when block sizes are unequal. Biometrika 58, 545-554. || 03. H.D. PATTERSON and R. THOMPSON. 1975. Maximum likelihood estimation of components of variance. Proceedings of the 8th International Biometric Conference. Ed. L.C.A. Corsten and T. Postelnicu, 199-207. || 04. R. THOMPSON. 1980. Maximum likelihood estimation of variance components. Math. Operationsforsh. Statist. ljU 545-561. || 05. R. THOMPSON. 1978. The estimation of variance and covariance components with an application when records are subject to culling. Biometrics 29, 527-550. || 06. L.R. SCHAEFFER, J.W. WILTON and R. THOMPSON. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34, 199-208. || 07. D.M. COOPER and R. THOMPSON. 1977 . A note on the estimation of the parameters of the autoregressive-moving average process. Biometrika 64, 625-628. || 08. R. THOMPSON. 1985. A note on restricted maximum likelihood estimation with an alternative outlier model. J.R. Statist. Soc. B 47, 53-55. || 09. R. THOMPSON. 1975. A note on the W transformation. Technometrics J7, 511-512. || 10. R. THOMPSON and K. MEYER. 1986. Estimation of variance components : what is missing in the EM algorithm? J. Statist. Comput. Simul. 24 215-230. || 11. D.L. ROBINSON, R. THOMPSON and P.G.N. DIGBY. REML. 1982. A program for the analysis of non-orthogonal data by restricted maximum likelihood. COMPSTAT 1982, II. Eds. H. Cassinus, P. Ettinger and J.R. Mattieu. Physica-Verlag, Wien 231-232. || 12. R. THOMPSON. 1983. Dial lei crosses, partially balanced incomplete block designs with triangular association schemes and rectangular lattices. GENSTAT newsletter JJ3, 16-32. || 13. R. THOMPSON. 1984. The use of multiple copies of data in forming and interpreting analysis of variance. Experimental design, Statistical Methods and Genetic Statistics. Ed. K. Hinkelmann. Marcel Dekker, New York, 155-174.GROUP II: APPLICATION OF STATISTICAL METHODS TO ANIMAL BREEDING STUDIES14. R. THOMPSON. 1976. The estimation of maternal genetic variances. Biometrics 32 903-917. || 15. R. THOMPSON. 1976. Design of experiments to estimate heritability when observations are available on parents and offspring. Biometrics 32 283-304. || 16. W.G. HILL and R. THOMPSON. 1977. Design of experiments to estimate parent-offspring regression using selected parents. Anim. Prod. 24, 163-168. || 17. N.D. CAMERON and R. THOMPSON. 1986. Design of multivariate selection experiments to estimate genetic parameters. Theor. Appl. Genet. 72, 466-476. || 18. R. THOMPSON. 1977. The estimation of heritability with unbalanced data. I. Observations available on parents and offspring. Biometrics 33, 485-495. || 19. R. THOMPSON. 1977. The estimation of heritability with unbalanced data. II. Data available on more than two generations. Biometrics 33, 495-504. || 20. R. THOMPSON. 1977. The estimation of heritability with unbalanced data. III. Unpublished Appendices, 1-17. || 21. R. THOMPSON. 1976. Estimation of quantitative genetic parameters. Proceedings of the International Conference on Quantitative Genetics. Ed. 0. Kempthorne, E. Pollak and T. Bailey. Iowa State University press, Ames, Iowa, 639-657. (vii) || 22. W.G. HILL and R. THOMPSON. 1978. Probabilities of non-positive definite between group or genetic covariance matrices. Biometrics 34, 429-439. || 23. K. MEYER and R. THOMPSON. 1984. Bias in variance and covariance component estimators due to selection on a correlated trait. Z. Tierzucht. Zuchtungsbiol. 101, 33-50. || 24. R. THOMPSON. 1976. Relationship between the cumulative different and best linear unbiased predictor methods of evaluating bulls. Anim. Prod. 23^, 15-24. || 25. R. THOMPSON. 1979. Sire Evaluation. Biometrics 35, 339-353. || 26. R. THOMPSON. 1986. Estimation of realised heritability in a selected population using mixed model methods. Genet. Sel. Evol . 475-484. || 27. R. THOMPSON. 1972. The maximum likelihood approach to the estimate of liability. Anim. Hum. Genet. 36, 221-231. || 28. R. THOMPSON, B.J. McGUIRK and A.R. GILMOUR. 1985. Estimating the heritability of all-or-none and categorical traits by offspring-parent regression. Z. Tierzucht. Zuchtungsbiol. 102, 342-354. || 29. J.L. FOULLEY, D. GIANOLA and R. THOMPSON. 1983. Prediction of genetic merit from data on binary and quantitative variates with an application to calving difficulty, birth weight and pelvic opening. Genet. Sel. Evol. 15, 401-424. || 30. R. THOMPSON and R.J. BAKER. 1981. Composite link functions in generalised linear models. J.R. Statist. Soc. B. 30, 125-131. || 31. R. THOMPSON. 1980. A note on the estimation of economic values for selection indices. Anim. Prod. 31, 115-117.GROUP III: EXPERIMENTAL STUDIES32. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1980. Genetic and evironmental influences on beef cattle production in Zambia. Factors affecting weaner production from Angoni, Barotse and Boran dams. Anim. Prod. 30, 217-234. || 33. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1980. Genetic and environmental influences on beef cattle production in Zambia. 2. Sire weights for age of purebred and reciprocally crossbred progeny. Anim. Prod. 30, 235-243. || 34. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1980. Genetic and environmental influences on beef cattle production in Zambia. 3. Carcass characteristics of purebred and reciprocally crossbred progeny. Anim. Prod. 30, 245-252. || 35. W. THORPE, D.C.K. CRUICKSHANK and R. THOMPSON. 1982. Genetic and environmental influences on beef cattle in Zambia. 4. Weaner production from purebred and reciprocally crossbred progeny. Anim. Prod. 33, 165-177. || 36. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1979. The growth and carcass character!- sti cs of crosses of Hereford and Friesian with Angoni, Barotse and Boran cattle in Zambia. J. Agric. Sci., Camb. 93, 423-430. || 37. I.L. MASON, V.E. VIAL and R. THOMPSON. 1972. Genetic parameters of beef characteristics and the genetic relationship between meat and milk production in British Friesian cattle. Anim. Prod. 135-148. || 38. W.G. HILL, M.R. EDWARDS, M-K A. AHMED and R. THOMPSON. 1983. Heritability of milk yield and composition at different levels and variability of production. Anim. Prod. 36, 59-68. || 39. V.P.S. CHAUHAN and R. THOMPSON. 1986. Dairy sire evaluation using a "rolling months" model. Z. Tierzucht. Zuchtungsbiol 103, 321-333

Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods

We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a $\tau-$mixing process.Comment: 39 page

Microbiome and Metagenomics: Statistical Methods, Computation and Applications

Human microbial communities are associated with many human diseases such as obesity, diabetes and inflammatory bowel disease. High-throughput sequencing technology has been widely used to profile the microbial communities in order to understand their impact on human health. In the first part of this dissertation, we analyzed fecal samples using shotgun metagenomic sequencing from a prospective cohort of pediatric Crohn\u27s disease patients, who started therapy with enteral nutrition or anti-TNF-alpha antibodies. The results reveal the full complement and dynamics of bacteria and fungi during treatment. Bacterial community membership was associated independently with dysbiosis, intestinal inflammation, antibiotic use, and therapy. Motivated by the problems in real data analysis, this dissertation also presents two novel statistical models for microbiome data analysis. One important aspect of metagenomic data analysis is to quantify the bacterial abundances based on the sequencing data. In order to account for certain systematic differences in read coverage along the genome, we propose a multi-sample Poisson model to quantify microbial abundances based on read counts that are assigned to species-specific taxonomic markers. Our model takes into account the marker-specific effects when normalizing the sequencing count data in order to obtain more accurate quantification of the species abundances. Another statistical model we proposed is for longitudinal microbiome data analysis. A key question in longitudinal microbiome studies is to identify the microbes that are associated with clinical outcomes or environmental factors. We develop a zero-inflated Beta regression model with random effects for testing the association between microbial abundance and clinical covariates for longitudinal microbiome data. The model includes a logistic regression component to model presence/absence of a microbe in samples and a Beta regression component to model non-zero microbial abundance, where each component includes a random effect to take into account the correlations among repeated measurements on the same subject. The statistical methods were evaluated using simulations as well as the real data from Penn microbiome study of pediatric Crohn\u27s disease

Statistical physics and epidemic inference: methods and applications

L'abstract è presente nell'allegato / the abstract is in the attachmen

Convergence rates of general regularization methods for statistical inverse problems and applications

During the past the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited by the fact that they require a complete spectral decomposition of the operator. Tikhonov estimators are simpler to compute, but still involve the inversion of an operator and achieve minimax rates only in restricted smoothness classes. In this paper we introduce a unifying technique to study the mean square error of a large class of regularization methods (spectral methods) including the aforementioned estimators as well as many iterative methods, such as í-methods and the Landweber iteration. The latter estimators converge at the same rate as spectral cut-off, but only require matrixvector products. Our results are applied to various problems, in particular we obtain precise convergence rates for satellite gradiometry, L2-boosting, and errors in variable problems. --Statistical inverse problems,iterative regularization methods,Tikhonov regularization,nonparametric regression,minimax convergence rates,satellite gradiometry,Hilbert scales,boosting,errors in variable