1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

On robust estimation of the location parameter

‡We describe the use of singular value decomposition in transforming genome-wide expression data from genes 3 arrays space to reduced diagonalized ‘‘eigengenes’’ 3 ‘‘eigenarrays’’ space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling

The main purpose of the present study is to use three state-of-the-art data mining techniques, namely, logistic model tree (LMT), random forest (RF), and classification and regression tree (CART) models, to map landslide susceptibility. Long County was selected as the study area. First, a landslide inventory map was constructed using history reports, interpretation of aerial photographs, and extensive field surveys. A total of 171 landslide locations were identified in the study area. Twelve landslide-related parameters were considered for landslide susceptibility mapping, including slope angle, slope aspect, plan curvature, profile curvature, altitude, NDVI, land use, distance to faults, distance to roads, distance to rivers, lithology, and rainfall. The 171 landslides were randomly separated into two groups with a 70/30 ratio for training and validation purposes, and different ratios of non-landslides to landslides grid cells were used to obtain the highest classification accuracy. The linear support vector machine algorithm (LSVM) was used to evaluate the predictive capability of the 12 landslide conditioning factors. Second, LMT, RF, and CART models were constructed using training data. Finally, the applied models were validated and compared using receiver operating characteristics (ROC), and predictive accuracy (ACC) methods. Overall, all three models exhibit reasonably good performances; the RF model exhibits the highest predictive capability compared with the LMT and CART models. The RF model, with a success rate of 0.837 and a prediction rate of 0.781, is a promising technique for landslide susceptibility mapping. Therefore, these three models are useful tools for spatial prediction of landslide susceptibility.

A comparative study of logistic model tree, random forest, and classification and regression tree models for spatial prediction of landslide susceptibility

Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis

Age at first marriage has an important impact on population growth rate. Modelling age at first marriage is very crucial since the growth rate of Bangladesh is very high. Here logistic regression model has been used for modelling age at first marriage using Bangladesh Demographic and Health Survey (BDHS-2011) data. The BDHS data was collected under two stage stratified sampling plan. That is why cluster correction and weight adjustment is necessary for analyzing this data. An extensive literature search fails to find the usage of these adjustments for modelling age at first marriage. In this paper, these two adjustments have been used for modelling and the prediction performance of the model has been measured by the training and test error.

Modelling Age at First Marriage of Female Adolescents in Bangladesh

Heritier S, Ronchetti E () Robust bounded-influence tests in general parametric models. J Am Stat Assoc :– Heritier S, Cantoni E, Copt S, Victoria-Feser M-P () Robust methods in biostatistics. Wiley, Chichester Huber PJ () Robust estimation of a location parameter. Ann Math Stat :– Huber PJ () A robust version of the probability ratio test. Ann Math Stat :– Huber PJ () Robust confidence limits. Z Wahrsch Verwandte Geb :– Huber PJ () Robust statistics. Wiley, New York Huber PJ, Ronchetti EM () Robust statistics, nd edn. Wiley, New York Huber PJ, Strassen V () Minimax tests and the Neyman-Pearson lemma for capacities. Ann Stat :–, :– Markatou M, Ronchetti E () Robust inference: the approach based on influence functions. In: Maddala GS, Rao CR (eds) Handbook of Statistics, vol . North Holland, Amsterdam, pp – Maronna RA, Martin RD, Yohai VJ () Robust statistics: theory and methods. Wiley, New York Ronchetti E () Robustheitseigenschaften von Tests. Diploma Thesis, ETH Zurich, Switzerland Ronchetti E () Robust testing in linear models: The infinitesimal approach. PhD Thesis, ETH Zurich, Switzerland Rousseeuw PJ, Ronchetti E () The influence curve for tests. Research report . Fachgruppe fur Statistik, ETH Zurich, Switzerland Schrader RM, Hettmansperger TP () Robust analysis of variance based upon a likelihood ratio criterion. Biometrika :– Tukey JW () A survey of sampling from contaminated distributions. In: Olkin I (ed) Contributions to probability and statistics. Stanford University Press, Stanford, pp –

Robust Regression Estimation in Generalized Linear Models.

In this paper, flfteen estimators of correlation coe‐cient available in the literature have been compared through simulation. We have considered simulating sampling distribution at bivariate standard normal and its flve contaminated forms with three difierent correlation coe‐cients and three difierent sample sizes. We also have considered a real population of size 1491.The estimators have been compared with regard to bias, standard error, mean square error and length of 90% percentile interval. The class of robust estimators, especially the normal score estimator has been found superior to the class of non-robust estimators over all. To measure correlation coe‐cient we have recommend using for normal score estimator especially when sample is large and contamination is probable.

Mohammed Nasser

Papers

Modelling Age at First Marriage of Female Adolescents in Bangladesh

Robust Regression Estimation in Generalized Linear Models.

Simulation Based Comparison among Fifteen Estimators of Correlation Coe-cient