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Full-Text Articles in Statistics and Probability
Regression Modeling And Prediction By Individual Observations Versus Frequency, Stan Lipovetsky
Regression Modeling And Prediction By Individual Observations Versus Frequency, Stan Lipovetsky
Journal of Modern Applied Statistical Methods
A regression model built by a dataset could sometimes demonstrate a low quality of fit and poor predictions of individual observations. However, using the frequencies of possible combinations of the predictors and the outcome, the same models with the same parameters may yield a high quality of fit and precise predictions for the frequencies of the outcome occurrence. Linear and logistical regressions are used to make an explicit exposition of the results of regression modeling and prediction.
Generalized Matrix Decomposition Regression: Estimation And Inference For Two-Way Structured Data, Yue Wang, Ali Shojaie, Tim Randolph, Jing Ma
Generalized Matrix Decomposition Regression: Estimation And Inference For Two-Way Structured Data, Yue Wang, Ali Shojaie, Tim Randolph, Jing Ma
UW Biostatistics Working Paper Series
Analysis of two-way structured data, i.e., data with structures among both variables and samples, is becoming increasingly common in ecology, biology and neuro-science. Classical dimension-reduction tools, such as the singular value decomposition (SVD), may perform poorly for two-way structured data. The generalized matrix decomposition (GMD, Allen et al., 2014) extends the SVD to two-way structured data and thus constructs singular vectors that account for both structures. While the GMD is a useful dimension-reduction tool for exploratory analysis of two-way structured data, it is unsupervised and cannot be used to assess the association between such data and an outcome of interest. …
Overcoming Small Data Limitations In Heart Disease Prediction By Using Surrogate Data, Alfeo Sabay, Laurie Harris, Vivek Bejugama, Karen Jaceldo-Siegl
Overcoming Small Data Limitations In Heart Disease Prediction By Using Surrogate Data, Alfeo Sabay, Laurie Harris, Vivek Bejugama, Karen Jaceldo-Siegl
SMU Data Science Review
In this paper, we present a heart disease prediction use case showing how synthetic data can be used to address privacy concerns and overcome constraints inherent in small medical research data sets. While advanced machine learning algorithms, such as neural networks models, can be implemented to improve prediction accuracy, these require very large data sets which are often not available in medical or clinical research. We examine the use of surrogate data sets comprised of synthetic observations for modeling heart disease prediction. We generate surrogate data, based on the characteristics of original observations, and compare prediction accuracy results achieved from …
Evaluating The Roc Performance Of Markers For Future Events, Margaret Pepe, Yingye Zheng, Yuying Jin
Evaluating The Roc Performance Of Markers For Future Events, Margaret Pepe, Yingye Zheng, Yuying Jin
UW Biostatistics Working Paper Series
Receiver operating characteristic (ROC) curves play a central role in the evaluation of biomarkers and tests for disease diagnosis. Predictors for event time outcomes can also be evaluated with ROC curves, but the time lag between marker measurement and event time must be acknowledged. We discuss different definitions of time-dependent ROC curves in the context of real applications. Several approaches have been proposed for estimation. We contrast retrospective versus prospective methods in regards to assumptions and flexibility, including their capacities to incorporate censored data, competing risks and different sampling schemes. Applications to two datasets are presented.
An Exploration Of Using Data Mining In Educational Research, Yonghong Jade Xu
An Exploration Of Using Data Mining In Educational Research, Yonghong Jade Xu
Journal of Modern Applied Statistical Methods
Technology advances popularized large databases in education. Traditional statistics have limitations for analyzing large quantities of data. This article discusses data mining by analyzing a data set with three models: multiple regression, data mining, and a combination of the two. It is concluded that data mining is applicable in educational research.
Deletion/Substitution/Addition Algorithm For Partitioning The Covariate Space In Prediction, Annette Molinaro, Mark J. Van Der Laan
Deletion/Substitution/Addition Algorithm For Partitioning The Covariate Space In Prediction, Annette Molinaro, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We propose a new method for predicting censored (and non-censored) clinical outcomes from a highly-complex covariate space. Previously we suggested a unified strategy for predictor construction, selection, and performance assessment. Here we introduce a new algorithm which generates a piecewise constant estimation sieve of candidate predictors based on an intensive and comprehensive search over the entire covariate space. This algorithm allows us to elucidate interactions and correlation patterns in addition to main effects.
Multiple Testing And Data Adaptive Regression: An Application To Hiv-1 Sequence Data, Merrill D. Birkner, Sandra E. Sinisi, Mark J. Van Der Laan
Multiple Testing And Data Adaptive Regression: An Application To Hiv-1 Sequence Data, Merrill D. Birkner, Sandra E. Sinisi, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Analysis of viral strand sequence data and viral replication capacity could potentially lead to biological insights regarding the replication ability of HIV-1. Determining specific target codons on the viral strand will facilitate the manufacturing of target specific antiretrovirals. Various algorithmic and analysis techniques can be applied to this application. We propose using multiple testing to find codons which have significant univariate associations with replication capacity of the virus. We also propose using a data adaptive multiple regression algorithm to obtain multiple predictions of viral replication capacity based on an entire mutant/non-mutant sequence profile. The data set to which these techniques …
Jmasm10: A Fortran Routine For Sieve Bootstrap Prediction Intervals, Andrés M. Alonso
Jmasm10: A Fortran Routine For Sieve Bootstrap Prediction Intervals, Andrés M. Alonso
Journal of Modern Applied Statistical Methods
A Fortran routine for constructing nonparametric prediction intervals for a general class of linear processes is described. The approach uses the sieve bootstrap procedure of Bühlmann (1997) based on residual resampling from an autoregressive approximation to the given process.
Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan
Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …
The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart
The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart
U.C. Berkeley Division of Biostatistics Working Paper Series
Suppose that we observe a sample of independent and identically distributed realizations of a random variable. Assume that the parameter of interest can be defined as the minimizer, over a suitably defined parameter space, of the expectation (with respect to the distribution of the random variable) of a particular (loss) function of a candidate parameter value and the random variable. Examples of commonly used loss functions are the squared error loss function in regression and the negative log-density loss function in density estimation. Minimizing the empirical risk (i.e., the empirical mean of the loss function) over the entire parameter space …
Loss-Based Estimation With Cross-Validation: Applications To Microarray Data Analysis And Motif Finding, Sandrine Dudoit, Mark J. Van Der Laan, Sunduz Keles, Annette M. Molinaro, Sandra E. Sinisi, Siew Leng Teng
Loss-Based Estimation With Cross-Validation: Applications To Microarray Data Analysis And Motif Finding, Sandrine Dudoit, Mark J. Van Der Laan, Sunduz Keles, Annette M. Molinaro, Sandra E. Sinisi, Siew Leng Teng
U.C. Berkeley Division of Biostatistics Working Paper Series
Current statistical inference problems in genomic data analysis involve parameter estimation for high-dimensional multivariate distributions, with typically unknown and intricate correlation patterns among variables. Addressing these inference questions satisfactorily requires: (i) an intensive and thorough search of the parameter space to generate good candidate estimators, (ii) an approach for selecting an optimal estimator among these candidates, and (iii) a method for reliably assessing the performance of the resulting estimator. We propose a unified loss-based methodology for estimator construction, selection, and performance assessment with cross-validation. In this approach, the parameter of interest is defined as the risk minimizer for a suitable …
Unified Cross-Validation Methodology For Selection Among Estimators And A General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities And Examples, Mark J. Van Der Laan, Sandrine Dudoit
Unified Cross-Validation Methodology For Selection Among Estimators And A General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities And Examples, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
In Part I of this article we propose a general cross-validation criterian for selecting among a collection of estimators of a particular parameter of interest based on n i.i.d. observations. It is assumed that the parameter of interest minimizes the expectation (w.r.t. to the distribution of the observed data structure) of a particular loss function of a candidate parameter value and the observed data structure, possibly indexed by a nuisance parameter. The proposed cross-validation criterian is defined as the empirical mean over the validation sample of the loss function at the parameter estimate based on the training sample, averaged over …
Estimating Predictors For Long- Or Short-Term Survivors, Lu Tian, Wei Wang, L. J. Wei
Estimating Predictors For Long- Or Short-Term Survivors, Lu Tian, Wei Wang, L. J. Wei
Harvard University Biostatistics Working Paper Series
No abstract provided.
Tree-Based Multivariate Regression And Density Estimation With Right-Censored Data , Annette M. Molinaro, Sandrine Dudoit, Mark J. Van Der Laan
Tree-Based Multivariate Regression And Density Estimation With Right-Censored Data , Annette M. Molinaro, Sandrine Dudoit, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We propose a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. This approach is entirely driven by the choice of a loss function for the full (uncensored) data structure and can be stated in terms of the following three main steps. (1) Define the parameter of interest as the minimizer of the expected loss, or risk, for a full data loss function chosen to represent the desired measure of performance. Map the full data loss function into an observed (censored) data loss function having the same expected value and leading to an efficient estimator …
Asymptotics Of Cross-Validated Risk Estimation In Estimator Selection And Performance Assessment, Sandrine Dudoit, Mark J. Van Der Laan
Asymptotics Of Cross-Validated Risk Estimation In Estimator Selection And Performance Assessment, Sandrine Dudoit, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Risk estimation is an important statistical question for the purposes of selecting a good estimator (i.e., model selection) and assessing its performance (i.e., estimating generalization error). This article introduces a general framework for cross-validation and derives distributional properties of cross-validated risk estimators in the context of estimator selection and performance assessment. Arbitrary classes of estimators are considered, including density estimators and predictors for both continuous and polychotomous outcomes. Results are provided for general full data loss functions (e.g., absolute and squared error, indicator, negative log density). A broad definition of cross-validation is used in order to cover leave-one-out cross-validation, V-fold …
Semi-Parametric Regression For The Area Under The Receiver Operating Characteristic Curve, Lori E. Dodd, Margaret S. Pepe
Semi-Parametric Regression For The Area Under The Receiver Operating Characteristic Curve, Lori E. Dodd, Margaret S. Pepe
UW Biostatistics Working Paper Series
Medical advances continue to provide new and potentially better means for detecting disease. Such is true in cancer, for example, where biomarkers are sought for early detection and where improvements in imaging methods may pick up the initial functional and molecular changes associated with cancer development. In other binary classification tasks, computational algorithms such as Neural Networks, Support Vector Machines and Evolutionary Algorithms have been applied to areas as diverse as credit scoring, object recognition, and peptide-binding prediction. Before a classifier becomes an accepted technology, it must undergo rigorous evaluation to determine its ability to discriminate between states. Characterization of …
The Analysis Of Placement Values For Evaluating Discriminatory Measures, Margaret S. Pepe, Tianxi Cai
The Analysis Of Placement Values For Evaluating Discriminatory Measures, Margaret S. Pepe, Tianxi Cai
UW Biostatistics Working Paper Series
The idea of using measurements such as biomarkers, clinical data, or molecular biology assays for classification and prediction is popular in modern medicine. The scientific evaluation of such measures includes assessing the accuracy with which they predict the outcome of interest. Receiver operating characteristic curves are commonly used for evaluating the accuracy of diagnostic tests. They can be applied more broadly, indeed to any problem involving classification to two states or populations (D = 0 or D = 1). We show that the ROC curve can be interpreted as a cumulative distribution function for the discriminatory measure Y in the …