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Articles 1 - 30 of 42
Full-Text Articles in Statistics and Probability
Jmasm 52: Extremely Efficient Permutation And Bootstrap Hypothesis Tests Using R, Christina Chatzipantsiou, Marios Dimitriadis, Manos Papadakis, Michail Tsagris
Jmasm 52: Extremely Efficient Permutation And Bootstrap Hypothesis Tests Using R, Christina Chatzipantsiou, Marios Dimitriadis, Manos Papadakis, Michail Tsagris
Journal of Modern Applied Statistical Methods
Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. Computationally efficient method for calculating permutation-based p-values for the Pearson correlation coefficient and two independent samples t-test are proposed. The method is general and can be applied to other similar two sample mean or two mean vectors cases.
Bayesian Analysis Of Extended Cox Model With Time-Varying Covariates Using Bootstrap Prior, Oyebayo R. Olaniran, Mohd Asrul A. Abdullah
Bayesian Analysis Of Extended Cox Model With Time-Varying Covariates Using Bootstrap Prior, Oyebayo R. Olaniran, Mohd Asrul A. Abdullah
Journal of Modern Applied Statistical Methods
A new Bayesian estimation procedure for extended cox model with time varying covariate was presented. The prior was determined using bootstrapping technique within the framework of parametric empirical Bayes. The efficiency of the proposed method was observed using Monte Carlo simulation of extended Cox model with time varying covariates under varying scenarios. Validity of the proposed method was also ascertained using real life data set of Stanford heart transplant. Comparison of the proposed method with its competitor established appreciable supremacy of the method.
Quasi-Likelihood Ratio Tests For Homoscedasticity In Linear Regression, Lili Yu, Varadan Sevilimedu, Robert Vogel, Hani Samawi
Quasi-Likelihood Ratio Tests For Homoscedasticity In Linear Regression, Lili Yu, Varadan Sevilimedu, Robert Vogel, Hani Samawi
Journal of Modern Applied Statistical Methods
Two quasi-likelihood ratio tests are proposed for the homoscedasticity assumption in the linear regression models. They require few assumptions than the existing tests. The properties of the tests are investigated through simulation studies. An example is provided to illustrate the usefulness of the new proposed tests.
A Flexible Zero-Inflated Poisson Regression Model, Eric S. Roemmele
A Flexible Zero-Inflated Poisson Regression Model, Eric S. Roemmele
Theses and Dissertations--Statistics
A practical problem often encountered with observed count data is the presence of excess zeros. Zero-inflation in count data can easily be handled by zero-inflated models, which is a two-component mixture of a point mass at zero and a discrete distribution for the count data. In the presence of predictors, zero-inflated Poisson (ZIP) regression models are, perhaps, the most commonly used. However, the fully parametric ZIP regression model could sometimes be restrictive, especially with respect to the mixing proportions. Taking inspiration from some of the recent literature on semiparametric mixtures of regressions models for flexible mixture modeling, we propose a …
Evaluation Of Using The Bootstrap Procedure To Estimate The Population Variance, Nghia Trong Nguyen
Evaluation Of Using The Bootstrap Procedure To Estimate The Population Variance, Nghia Trong Nguyen
Electronic Theses and Dissertations
The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a …
Jmasm44: Implementing Multiple Ratio Imputation By The Emb Algorithm (R), Masayoshi Takahashi
Jmasm44: Implementing Multiple Ratio Imputation By The Emb Algorithm (R), Masayoshi Takahashi
Journal of Modern Applied Statistical Methods
Although single ratio imputation is often used to deal with missing values in practice, there is a paucity of discussion regarding multiple ratio imputation. Code in the R statistical environment is presented to execute multiple ratio imputation by the Expectation-Maximization with Bootstrapping (EMB) algorithm.
Multiple Ratio Imputation By The Emb Algorithm: Theory And Simulation, Masayoshi Takahashi
Multiple Ratio Imputation By The Emb Algorithm: Theory And Simulation, Masayoshi Takahashi
Journal of Modern Applied Statistical Methods
Although multiple imputation is the gold standard of treating missing data, single ratio imputation is often used in practice. Based on Monte Carlo simulation, the Expectation-Maximization with Bootstrapping (EMB) algorithm to create multiple ratio imputation is used to fill in the gap between theory and practice.
On Some Test Statistics For Testing The Population Skewness And Kurtosis: An Empirical Study, Yawen Guo
On Some Test Statistics For Testing The Population Skewness And Kurtosis: An Empirical Study, Yawen Guo
FIU Electronic Theses and Dissertations
The purpose of this thesis is to propose some test statistics for testing the skewness and kurtosis parameters of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results for testing the skewness parameter indicate that the power of the tests differs significantly across sample sizes, the …
A Review Of Frequentist Tests For The 2x2 Binomial Trial, Chris Lloyd
A Review Of Frequentist Tests For The 2x2 Binomial Trial, Chris Lloyd
Chris J. Lloyd
The 2x2 binomial trial is the simplest of data structures yet its statistical analysis and the issues it raises have been debated and revisited for over 70 years. Which analysis should biomedical researchers use in applications? In this review, we consider frequentist tests only, specifically tests with control size either exactly or very close to exactly. These procedures can be classified as conditional and unconditional. Amongst tests motivated by a conditional model, Lancaster’s mid-p and Liebermeister’s test are less conservative than Fisher’s classical test, but do not control type 1 error. Within the conditional framework, only Fisher’s test can be …
Constructing Confidence Intervals For Effect Sizes In Anova Designs, Li-Ting Chen, Chao-Ying Joanne Peng
Constructing Confidence Intervals For Effect Sizes In Anova Designs, Li-Ting Chen, Chao-Ying Joanne Peng
Journal of Modern Applied Statistical Methods
A confidence interval for effect sizes provides a range of plausible population effect sizes (ES) that are consistent with data. This article defines an ES as a standardized linear contrast of means. The noncentral method, Bonett’s method, and the bias-corrected and accelerated bootstrap method are illustrated for constructing the confidence interval for such an effect size. Results obtained from the three methods are discussed and interpretations of results are offered.
Bootstrap Interval Estimation Of Reliability Via Coefficient Omega, Miguel A. Padilla, Jasmin Divers
Bootstrap Interval Estimation Of Reliability Via Coefficient Omega, Miguel A. Padilla, Jasmin Divers
Journal of Modern Applied Statistical Methods
Three different bootstrap confidence intervals (CIs) for coefficient omega were investigated. The CIs were assessed through a simulation study with conditions not previously investigated. All methods performed well; however, the normal theory bootstrap (NTB) CI had the best performance because it had more consistent acceptable coverage under the simulation conditions investigated.
Theory And Methods For Gini Coefficients Partitioned By Quantile Range, Chaitra Nagaraja
Theory And Methods For Gini Coefficients Partitioned By Quantile Range, Chaitra Nagaraja
Chaitra H Nagaraja
The Gini coefficient is frequently used to measure inequality in populations. However, it is possible that inequality levels may change over time differently for disparate subgroups which cannot be detected with population-level estimates only. Therefore, it may be informative to examine inequality separately for these segments. The case where the population is split into two segments based on non-overlapping quantile ranges is examined. Asymptotic theory is derived and practical methods to estimate standard errors and construct confidence intervals using resampling methods are developed. An application to per capita income across census tracts using American Community Survey data is considered.
The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
Journal of Modern Applied Statistical Methods
The length-biased version of the lognormal distribution and related estimation problems are considered and sized-biased data arising in the exploration of oil fields is analyzed. The properties of the estimators are studied using simulations and the use of sample mode as an estimate of the lognormal parameter is discussed.
Empirical Sampling From Permutation Space With Unique Patterns, Justice I. Odiase
Empirical Sampling From Permutation Space With Unique Patterns, Justice I. Odiase
Journal of Modern Applied Statistical Methods
The exact distribution of a test statistic ultimately guarantees that the probability of a Type I error is exactly α. Several methods for estimating the exact distribution of a test statistic have evolved over the years with inherent computational problems and varying degrees of accuracy. The unique pattern of permutations resulting from using experimental data to sample within the permutation space without the risk of repeating permutations is identified. The method presented circumvents the theoretical requirements of asymptotic procedures and the computational difficulties associated with an exhaustive enumeration of permutations. Results show that time and space complexities are drastically reduced …
Modeling Repairable System Failures With Interval Failure Data And Time Dependent Covariate, Jayanthi Arasan, Samira Ehsani
Modeling Repairable System Failures With Interval Failure Data And Time Dependent Covariate, Jayanthi Arasan, Samira Ehsani
Journal of Modern Applied Statistical Methods
An application of a repairable system model for interval failure data with a time dependent covariate is examined. The performance of several models based on the NHPP when applied to real data on ball bearing failures is also explored. The best model for the data was selected based on results of the likelihood ratio test. The bootstrapping technique was applied to obtain the variance estimate for the estimated expected number of failures. Results demonstrate that the proposed model works well and is easy to implement, in addition the bootstrap variance estimate provides a simple substitute for the traditional estimate.
Weighting Large Datasets With Complex Sampling Designs: Choosing The Appropriate Variance Estimation Method, Sara Mann, James Chowhan
Weighting Large Datasets With Complex Sampling Designs: Choosing The Appropriate Variance Estimation Method, Sara Mann, James Chowhan
Journal of Modern Applied Statistical Methods
Using the Canadian Workplace and Employee Survey (WES), three variance estimation methods for weighting large datasets with complex sampling designs are compared: simple final weighting, standard bootstrapping and mean bootstrapping. Using a logit analysis, it is shown - depending on which weighting method is used - different predictor variables are significant. The potential lack of independence inherent in a multi-stage cluster sample design, as in the WES, results in a downward bias in the variance when conducting statistical inference (using the simple final weight), which in turn results in increased Type I errors. Bootstrap methods can account for the survey’s …
Generalized Variances Ratio Test For Comparing K Covariance Matrices From Dependent Normal Populations, Marcelo Angelo Cirillo, Daniel Furtado Ferreira, Thelma Sáfadi, Eric Batista Ferreira
Generalized Variances Ratio Test For Comparing K Covariance Matrices From Dependent Normal Populations, Marcelo Angelo Cirillo, Daniel Furtado Ferreira, Thelma Sáfadi, Eric Batista Ferreira
Journal of Modern Applied Statistical Methods
New tests based on the ratio of generalized variances are presented to compare covariance matrices from dependent normal populations. Monte Carlo simulation concluded that the tests considered controlled the Type I error, providing empirical probabilities that were consistent with the nominal level stipulated.
Another Look At Resampling: Replenishing Small Samples With Virtual Data Through S-Smart, Haiyan Bai, Wei Pan, Leigh Lihshing Wang, Phillip Neal Ritchey
Another Look At Resampling: Replenishing Small Samples With Virtual Data Through S-Smart, Haiyan Bai, Wei Pan, Leigh Lihshing Wang, Phillip Neal Ritchey
Journal of Modern Applied Statistical Methods
A new resampling method is introduced to generate virtual data through a smoothing technique for replenishing small samples. The replenished analyzable sample retains the statistical properties of the original small sample, has small standard errors and possesses adequate statistical power.
Level Robust Methods Based On The Least Squares Regression Estimator, Marie Ng, Rand R. Wilcox
Level Robust Methods Based On The Least Squares Regression Estimator, Marie Ng, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Heteroscedastic consistent covariance matrix (HCCM) estimators provide ways for testing hypotheses about regression coefficients under heteroscedasticity. Recent studies have found that methods combining the HCCM-based test statistic with the wild bootstrap consistently perform better than non-bootstrap HCCM-based methods (Davidson & Flachaire, 2008; Flachaire, 2005; Godfrey, 2006). This finding is more closely examined by considering a broader range of situations which were not included in any of the previous studies. In addition, the latest version of HCCM, HC5 (Cribari-Neto, et al., 2007), is evaluated.
The Bootstrap Method For The Selection Of A Shrinkage Factor In Two-Stage Estimation Of The Reliability Function Of An Exponential Distribution, Makarand V. Ratnaparkhi, Vasant B. Waikar, Fredrick J. Schuurmann
The Bootstrap Method For The Selection Of A Shrinkage Factor In Two-Stage Estimation Of The Reliability Function Of An Exponential Distribution, Makarand V. Ratnaparkhi, Vasant B. Waikar, Fredrick J. Schuurmann
Journal of Modern Applied Statistical Methods
An application of a bootstrap method for selecting a suitable shrinkage factor for the two-stage shrinkage estimator of a reliability function for the exponential distribution is discussed. The estimator obtained here has higher efficiency as compared to the one where the shrinkage factor is not subjected to bootstrapping.
Constructing Confidence Intervals For Spearman’S Rank Correlation With Ordinal Data: A Simulation Study Comparing Analytic And Bootstrap Methods, John Ruscio
Journal of Modern Applied Statistical Methods
Research shows good probability coverage using analytic confidence intervals (CIs) for Spearman’s rho with continuous data, but poorer coverage with ordinal data. A simulation study examining the latter case replicated prior results and revealed that coverage of bootstrap CIs was usually as good or better than coverage of analytic CIs.
A Simple Method For Finding Emperical Liklihood Type Intervals For The Roc Curve, Ayman Baklizi
A Simple Method For Finding Emperical Liklihood Type Intervals For The Roc Curve, Ayman Baklizi
Journal of Modern Applied Statistical Methods
Interval estimation of the ROC curve is considered using the empirical likelihood techniques. Suggested is a procedure that is very simple computationally and avoids the constrained optimization problems usually faced with empirical likelihood methods. Various modifications are suggested and the performance of the intervals is evaluated in terms of their coverage probability. The results show that some of the suggested intervals compete well with other intervals known in the literature.
Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade
Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade
Journal of Modern Applied Statistical Methods
Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-and-neck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution.
Comparing The Statistical Tests For Homogeneity Of Variances., Zhiqiang Mu
Comparing The Statistical Tests For Homogeneity Of Variances., Zhiqiang Mu
Electronic Theses and Dissertations
Testing the homogeneity of variances is an important problem in many applications since statistical methods of frequent use, such as ANOVA, assume equal variances for two or more groups of data. However, testing the equality of variances is a difficult problem due to the fact that many of the tests are not robust against non-normality. It is known that the kurtosis of the distribution of the source data can affect the performance of the tests for variance. We review the classical tests and their latest, more robust modifications, some other tests that have recently appeared in the literature, and use …
Empirical Likelihood Inference For The Area Under The Roc Curve, Gengsheng Qin, Xiao-Hua Zhou
Empirical Likelihood Inference For The Area Under The Roc Curve, Gengsheng Qin, Xiao-Hua Zhou
UW Biostatistics Working Paper Series
For a continuous-scale diagnostic test, the most commonly used summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC) that measures the accuracy of the diagnostic test. In this paper we propose an empirical likelihood approach for the inference of AUC. We first define an empirical likelihood ratio for AUC and show that its limiting distribution is a scaled chi-square distribution. We then obtain an empirical likelihood based confidence interval for AUC using the scaled chi-square distribution. This empirical likelihood inference for AUC can be extended to stratified samples and the resulting limiting distribution …
Large Sample And Bootstrap Intervals For The Gamma Scale Parameter Based On Grouped Data, Ayman Baklizi, Amjad Al-Nasser
Large Sample And Bootstrap Intervals For The Gamma Scale Parameter Based On Grouped Data, Ayman Baklizi, Amjad Al-Nasser
Journal of Modern Applied Statistical Methods
Interval estimation of the scale parameter of the gamma distribution using grouped data is considered in this article. Exact intervals do not exist and approximate intervals are needed Recently, Chen and Mi (2001) proposed alternative approximate intervals. In this article, some bootstrap and jackknife type intervals are proposed. The performance of these intervals is investigated and compared. The results show that some of the suggested intervals have a satisfactory statistical performance in situations where the sample size is small with heavy proportion of censoring.
Second-Order Accurate Inference On Simple, Partial, And Multiple Correlations, Robert J. Boik, Ben Haaland
Second-Order Accurate Inference On Simple, Partial, And Multiple Correlations, Robert J. Boik, Ben Haaland
Journal of Modern Applied Statistical Methods
This article develops confidence interval procedures for functions of simple, partial, and squared multiple correlation coefficients. It is assumed that the observed multivariate data represent a random sample from a distribution that possesses infinite moments, but there is no requirement that the distribution be normal. The coverage error of conventional one-sided large sample intervals decreases at rate 1√n as n increases, where n is an index of sample size. The coverage error of the proposed intervals decreases at rate 1/n as n increases. The results of a simulation study that evaluates the performance of the proposed intervals is …
Test Statistics Null Distributions In Multiple Testing: Simulation Studies And Applications To Genomics, Katherine S. Pollard, Merrill D. Birkner, Mark J. Van Der Laan, Sandrine Dudoit
Test Statistics Null Distributions In Multiple Testing: Simulation Studies And Applications To Genomics, Katherine S. Pollard, Merrill D. Birkner, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
Multiple hypothesis testing problems arise frequently in biomedical and genomic research, for instance, when identifying differentially expressed or co-expressed genes in microarray experiments. We have developed generally applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for control of a broad class of Type I error rates, defined as tail probabilities and expected values for arbitrary functions of the numbers of false positives and rejected hypotheses (Dudoit and van der Laan, 2005; Dudoit et al., 2004a,b; Pollard and van der Laan, 2004; van der Laan et al., 2005, 2004a,b). As argued in the early article of Pollard and van der …
Testing The Goodness Of Fit Of Multivariate Multiplicative-Intercept Risk Models Based On Case-Control Data, Biao Zhang
Testing The Goodness Of Fit Of Multivariate Multiplicative-Intercept Risk Models Based On Case-Control Data, Biao Zhang
Journal of Modern Applied Statistical Methods
The validity of the multivariate multiplicative-intercept risk model with I +1 categories based on casecontrol data is tested. After reparametrization, the assumed risk model is equivalent to an (I +1) -sample semiparametric model in which the I ratios of two unspecified density functions have known parametric forms. By identifying this (I +1) -sample semiparametric model, which is of intrinsic interest in general (I +1) -sample problems, with an (I +1) -sample semiparametric selection bias model, we propose a weighted Kolmogorov-Smirnov-type statistic to test the validity of the multivariate multiplicativeintercept risk model. Established are some asymptotic results …
Two Sides Of The Same Coin: Bootstrapping The Restricted Vs. Unrestricted Model, Panagiotis Mantalos
Two Sides Of The Same Coin: Bootstrapping The Restricted Vs. Unrestricted Model, Panagiotis Mantalos
Journal of Modern Applied Statistical Methods
The properties of the bootstrap test for restrictions are studied in two versions: 1) bootstrapping under the null hypothesis, restricted, and 2) bootstrapping under the alternative hypothesis, unrestricted. This article demonstrates the equivalence of these two methods, and illustrates the small sample properties of the Wald test for testing Granger-Causality in a stable stationary VAR system by Monte Carlo methods. The analysis regarding the size of the test reveals that, as expected, both bootstrap tests have actual sizes that lie close to the nominal size. Regarding the power of the test, the Wald and bootstrap tests share the same power …