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Articles 511 - 540 of 1633
Full-Text Articles in Statistical Theory
Robust Winsorized Shrinkage Estimators For Linear Regression Model, Nileshkumar H. Jadhav, D N. Kashid
Robust Winsorized Shrinkage Estimators For Linear Regression Model, Nileshkumar H. Jadhav, D N. Kashid
Journal of Modern Applied Statistical Methods
In multiple linear regression, the ordinary least squares estimator is very sensitive to the presence of multicollinearity and outliers in the response variable. To handle these problems in the data, Winsorized shrinkage estimators are proposed and the performance of these estimators is evaluated through mean square error sense.
Discrete Generalized Burr-Type Xii Distribution, B. A. Para, T. R. Jan
Discrete Generalized Burr-Type Xii Distribution, B. A. Para, T. R. Jan
Journal of Modern Applied Statistical Methods
A discrete analogue of generalized Burr-type XII distribution is introduced using a general approach of discretizing a continuous distribution. It may be worth exploring the possibility of developing a discrete version of the six parameter generalized Burr-type XII distribution for use in modeling a discrete data. This distribution is suggested as a suitable reliability model to fit a range of discrete lifetime data, as it is shown that hazard rate function can attain monotonic increasing (deceasing) shape for certain values of parameters. The equivalence of discrete generalized Burr-type XII (DGBD-XII) and continuous generalized Burr-type XII (GBD-XII) distributions has been established. …
Bayesian Estimation Of The Parameters Of Two-Component Mixture Of Rayleigh Distribution Under Doubly Censoring, Tahassum N. Sindhu, Navid Feroze, Muhammad Aslam
Bayesian Estimation Of The Parameters Of Two-Component Mixture Of Rayleigh Distribution Under Doubly Censoring, Tahassum N. Sindhu, Navid Feroze, Muhammad Aslam
Journal of Modern Applied Statistical Methods
Recently, the Bayesian analysis of the two-component mixture of lifetime models under singly type I censored samples was discussed. The Bayes estimation of the parameters of mixture of two Rayleigh distributions (MTRD) is developed under doubly censoring. Different informative priors, under squared error loss function and k-loss function, have been assumed for the posterior estimation. The performance of different estimators has been compared in terms of posterior risks by analyzing the simulated and real life data sets.
Survival Estimation Using Bootstrap, Jackknife And K-Repeated Jackknife Methods, Johnson A. Adewara, Ugochukwu A. Mbata
Survival Estimation Using Bootstrap, Jackknife And K-Repeated Jackknife Methods, Johnson A. Adewara, Ugochukwu A. Mbata
Journal of Modern Applied Statistical Methods
Three re-sampling techniques are used to estimate the survival probabilities from an exponential life-time distribution. The aim is to employ a technique to obtain a parameter estimate for a two-parameter exponential distribution. The re-sampling methods considered are: Bootstrap estimation method (BE), Jackknife estimation method (JE) and the k-repeated Jackknife estimation method (KJE). The methods were computed to obtain the mean square error (MSE) and mean percentage error (MPE) based on simulated data. The estimates of the two-parameter exponential distribution were substituted to estimate survival probabilities. Results show that the MSE value is reduced when the K–repeated jackknife method …
Some Methods Of Estimation From Censored Samples In Exponential And Gamma Models, R R. L Kantam, B Sriram
Some Methods Of Estimation From Censored Samples In Exponential And Gamma Models, R R. L Kantam, B Sriram
Journal of Modern Applied Statistical Methods
Two popular life testing models exponential and one where its generalization is gamma are considered. Estimation of scale parameter from a general Type-II doubly censored sample is attempted by the principle of maximum likelihood method. Resulting equations found to be giving iterative solutions. As an alternative to iterative solution certain admissible modifications to the estimating equations are suggested in special cases. The resulting estimates are compared with the exact maximum likelihood estimates analytically or through simulation. The results are also extended for reliability estimation.
Vol. 13, No. 2 (Full Issue), Jmasm Editors
Vol. 13, No. 2 (Full Issue), Jmasm Editors
Journal of Modern Applied Statistical Methods
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Comparison Of Estimators In Glm With Binary Data, D. M. Sakate, D. N. Kashid
Comparison Of Estimators In Glm With Binary Data, D. M. Sakate, D. N. Kashid
Journal of Modern Applied Statistical Methods
Maximum likelihood estimates (MLE) of regression parameters in the generalized linear models (GLM) are biased and their bias is non negligible when sample size is small. This study focuses on the GLM with binary data with multiple observations on response for each predictor value when sample size is small. The performance of the estimation methods in Cordeiro and McCullagh (1991), Firth (1993) and Pardo et al. (2005) are compared for GLM with binary data using an extensive Monte Carlo simulation study. Performance of these methods for three real data sets is also compared.
Life Testing Analysis Of Failure Censored Generalized Exponentiated Data, Anwar Hassan, Mehraj Ahmad
Life Testing Analysis Of Failure Censored Generalized Exponentiated Data, Anwar Hassan, Mehraj Ahmad
Journal of Modern Applied Statistical Methods
A generalized exponential distribution is considered for analyzing lifetime data; such statistical models are applicable when the observations are available in an ordered manner. This study examines failure censored data, which consist of testing n items and terminating the experiment when a pre-assigned number of items, for example r ( < n), have failed. Due to scale and shape parameters, both have flexibility for analyzing different types of lifetime data. This distribution has increasing, decreasing and a constant hazard rate depending on the shape parameter. This study provides maximum likelihood estimation and uniformly minimum variance unbiased techniques for the estimation of reliability of a component. Numerical computation was conducted on a data set and a comparison of the performance of two different techniques is presented.
Ridge Regression And Ill-Conditioning, Ghadban Khalaf, Mohamed Iguernane
Ridge Regression And Ill-Conditioning, Ghadban Khalaf, Mohamed Iguernane
Journal of Modern Applied Statistical Methods
Hoerl and Kennard (1970) suggested the ridge regression estimator as an alternative to the Ordinary Least Squares (OLS) estimator in the presence of multicollinearity. This article proposes new methods for estimating the ridge parameter in case of ordinary ridge regression. A simulation study evaluates the performance of the proposed estimators based on the Mean Squared Error (MSE) criterion and indicates that, under certain conditions, the proposed estimators perform well compared to the OLS estimator and another well-known estimator reviewed.
Estimation Of Multi Component Systems Reliability In Stress-Strength Models, Adil H. Khan, T R. Jan
Estimation Of Multi Component Systems Reliability In Stress-Strength Models, Adil H. Khan, T R. Jan
Journal of Modern Applied Statistical Methods
In a system with standby redundancy, there are a number of components only one of which works at a time and the other remain as standbys. When an impact of stress exceeds the strength of the active component, for the first time, it fails and another from standbys, if there is any, is activated and faces the impact of stresses, not necessarily identical as faced by the preceding component and the system fails when all the components have failed. Sriwastav and Kakaty (1981) assumed that the components stress-strengths are similarly distributed. However, in general the stress distributions will …
Estimation Of Gumbel Parameters Under Ranked Set Sampling, Omar M. Yousef, Sameer A. Al-Subh
Estimation Of Gumbel Parameters Under Ranked Set Sampling, Omar M. Yousef, Sameer A. Al-Subh
Journal of Modern Applied Statistical Methods
Consider the MLEs (maximum likelihood estimators) of the parameters of the Gumbel distribution using SRS (simple random sample) and RSS (ranked set sample) and the MOMEs (method of moment estimators) and REGs (regression estimators) based on SRS. A comparison between these estimators using bias and MSE (mean square error) was performed using simulation. It appears that the MLE based on RSS can be a robust competitor to the MLE based on SRS.
Estimates And Forecasts Of Garch Model Under Misspecified Probability Distributions: A Monte Carlo Simulation Approach, Olaoluwa S. Yaya, Olusanya E. Olubusoye, Oluwadare O. Ojo
Estimates And Forecasts Of Garch Model Under Misspecified Probability Distributions: A Monte Carlo Simulation Approach, Olaoluwa S. Yaya, Olusanya E. Olubusoye, Oluwadare O. Ojo
Journal of Modern Applied Statistical Methods
The effect of misspecification of correct sampling probability distribution of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) processes is considered. The three assumed distributions are the normal, Student t, and generalized error distributions. The GARCH process is sampled using one of the distributions and the model is estimated based on the three distributions in each sample. Parameter estimates and forecast performance are used to judge the estimated model for performance. The AR-GARCH-GED performed better on the three assumed distributions; even, when Student t distribution is assumed, AR-GARCH-Student t does not perform as the best model.
End Matter, Jmasm Editors
Double Bootstrap Confidence Interval Estimates With Censored And Truncated Data, Jayanthi Arasan, Mohd B. Adam
Double Bootstrap Confidence Interval Estimates With Censored And Truncated Data, Jayanthi Arasan, Mohd B. Adam
Journal of Modern Applied Statistical Methods
Traditional inferential procedures often fail with censored and truncated data, especially when sample sizes are small. In this paper we evaluate the performances of the double and single bootstrap interval estimates by comparing the double percentile (DB-p), double percentile-t (DB-t), single percentile (B-p), and percentile-t (B-t) bootstrap interval estimation methods via a coverage probability study when the data is censored using the log logistic model. We then apply the double bootstrap intervals to real right censored lifetime data on 32 women with breast cancer and failure data on 98 brake pads where all the observations were left truncated.
Interadapt -- An Interactive Tool For Designing And Evaluating Randomized Trials With Adaptive Enrollment Criteria, Aaron Joel Fisher, Harris Jaffee, Michael Rosenblum
Interadapt -- An Interactive Tool For Designing And Evaluating Randomized Trials With Adaptive Enrollment Criteria, Aaron Joel Fisher, Harris Jaffee, Michael Rosenblum
Johns Hopkins University, Dept. of Biostatistics Working Papers
The interAdapt R package is designed to be used by statisticians and clinical investigators to plan randomized trials. It can be used to determine if certain adaptive designs offer tangible benefits compared to standard designs, in the context of investigators’ specific trial goals and constraints. Specifically, interAdapt compares the performance of trial designs with adaptive enrollment criteria versus standard (non-adaptive) group sequential trial designs. Performance is compared in terms of power, expected trial duration, and expected sample size. Users can either work directly in the R console, or with a user-friendly shiny application that requires no programming experience. Several added …
Targeted Maximum Likelihood Estimation Using Exponential Families, Iván Díaz, Michael Rosenblum
Targeted Maximum Likelihood Estimation Using Exponential Families, Iván Díaz, Michael Rosenblum
Johns Hopkins University, Dept. of Biostatistics Working Papers
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We investigate the use of exponential families to define the parametric submodel. This implementation of TMLE gives a general approach for estimating any smooth parameter in the nonparametric model. A computational advantage of this approach is that each iteration of TMLE involves estimation of a parameter in an exponential family, which is a convex optimization problem for which software implementing reliable and computationally efficient methods exists. We illustrate …
Bias And Precision Of The Squared Canonical Correlation Coefficient Under Nonnormal Data Condition, Lesley F. Leach, Robin K. Henson
Bias And Precision Of The Squared Canonical Correlation Coefficient Under Nonnormal Data Condition, Lesley F. Leach, Robin K. Henson
Journal of Modern Applied Statistical Methods
Monte Carlo methods were employed to investigate the effect of nonnormality on the bias associated with the squared canonical correlation coefficient (Rc2). The majority of Rc2 estimates were found to be extremely biased, but the magnitude of bias was impacted little by the degree of nonnormality.
Stochastic Randomized Response Model For A Quantitative Sensitive Random Variable, Sarjinder Singh, Stephen A. Sedory
Stochastic Randomized Response Model For A Quantitative Sensitive Random Variable, Sarjinder Singh, Stephen A. Sedory
Journal of Modern Applied Statistical Methods
A new stochastic randomized response model is introduced that is useful for estimating the population mean of a sensitive quantitative variable. The proposed stochastic randomized response model is an extension of the stochastic randomized response model from a qualitative sensitive variable to a quantitative variable found in Singh (2002). The stochastic nature of a randomized response device helps increase a respondent’s cooperation while collecting information on sensitive variables in a society. The Bar-Lev, Bobovitch, and Boukai (2004) model is shown to be a special case of the proposed model.
Ridge Regression In Calibration Models With Symmetric Padding Extension-Daubechies Wavelet Transform Preprocessing, Nurwiani, S Sunaryo, Setiawan, B W. Otok
Ridge Regression In Calibration Models With Symmetric Padding Extension-Daubechies Wavelet Transform Preprocessing, Nurwiani, S Sunaryo, Setiawan, B W. Otok
Journal of Modern Applied Statistical Methods
Wavelet transformation is commonly used in calibration models as a preprocessing step. This preprocessing does not involve all results of a spectrum discretization; consequently, a lot of information can be missing. To avoid missing information, a symmetric padding extension (SPE) can be used to place all data points into dyadic scales, however, high dimensional discretization points need to be reduced. Dimension reduction can be performed with Daubechies wavelet transformation (DWT). Scale function and Daubechies wavelet are continuous functions, thus they perform a faster approximation. SPE-DWT preprocessing combines SPE and DWT. Multicollinearity often occurs in calibration models; the ridge regression (RR) …
Statistical Power Of Alternative Structural Models For Comparative Effectiveness Research: Advantages Of Modeling Unreliability, Emil N. Coman, Eugen Iordache, Lisa Dierker, Judith Fifield, Jean J. Schensul, Suzanne Suggs, Russell Barbour
Statistical Power Of Alternative Structural Models For Comparative Effectiveness Research: Advantages Of Modeling Unreliability, Emil N. Coman, Eugen Iordache, Lisa Dierker, Judith Fifield, Jean J. Schensul, Suzanne Suggs, Russell Barbour
Journal of Modern Applied Statistical Methods
The advantages of modeling the unreliability of outcomes when evaluating the comparative effectiveness of health interventions is illustrated. Adding an action-research intervention component to a regular summer job program for youth was expected to help in preventing risk behaviors. A series of simple two-group alternative structural equation models are compared to test the effect of the intervention on one key attitudinal outcome in terms of model fit and statistical power with Monte Carlo simulations. Some models presuming parameters equal across the intervention and comparison groups were under- powered to detect the intervention effect, yet modeling the unreliability of the outcome …
A Flexible Method For Conducting Power Analysis For Two- And Three-Level Hierarchical Linear Models In R, Yi Pan, Matthew T. Mcbee
A Flexible Method For Conducting Power Analysis For Two- And Three-Level Hierarchical Linear Models In R, Yi Pan, Matthew T. Mcbee
Journal of Modern Applied Statistical Methods
A general approach for conducting power analysis in two- and three-level hierarchical linear models (HLMs) is described. The method can be used to perform power analysis to detect fixed effects at any level of a HLM with dichotomous or continuous covariates. It can easily be extended to perform power analysis for functions of parameters. Important steps in the derivation of this approach are illustrated and numerical examples are provided. Sample code implementing this approach is provided using the free program R.
Estimation Of Reliability In Multicomponent Stress-Strength Based On Generalized Rayleigh Distribution, Gadde Srinivasa Rao
Estimation Of Reliability In Multicomponent Stress-Strength Based On Generalized Rayleigh Distribution, Gadde Srinivasa Rao
Journal of Modern Applied Statistical Methods
A multicomponent system of k components having strengths following k- independently and identically distributed random variables x1, x2, ..., xk and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by a generalized Rayleigh distribution with different shape parameters. Reliability is estimated using the maximum likelihood (ML) method of estimation in samples drawn from strength and stress …
Specifying Asymmetric Star Models With Linear And Nonlinear Garch Innovations: Monte Carlo Approach, Olaoluwa S. Yaya, Olanrewaju I. Shittu
Specifying Asymmetric Star Models With Linear And Nonlinear Garch Innovations: Monte Carlo Approach, Olaoluwa S. Yaya, Olanrewaju I. Shittu
Journal of Modern Applied Statistical Methods
Economic and finance time series are typically asymmetric and are expected to be modeled using asymmetrical nonlinear time series models. Smooth Transition Autoregressive (STAR) models: Logistic (LSTAR) and Exponential (ESTAR) are known to be asymmetric and symmetric respectively. Under non-normal and heteroscedastic innovations, the residuals of these models are estimated using Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models with variants which include linear and nonlinear forms. The small sample properties of STAR-GARCH variants are yet to be established but these properties are investigated using Monte Carlo (MC) simulation. An MC investigation was conducted to investigate the performance of selections of STAR-GARCH …
Robustness Of Several Estimators Of The Acf Of Ar(1) Process With Non-Gaussian Errors, A A. Smadi, J J. Jaber, A G. Al-Zu'bi
Robustness Of Several Estimators Of The Acf Of Ar(1) Process With Non-Gaussian Errors, A A. Smadi, J J. Jaber, A G. Al-Zu'bi
Journal of Modern Applied Statistical Methods
The autocorrelation function (ACF) plays an important role in the context of ARMA modeling, especially for their identification and estimation. This study considers the robust estimation of the ACF of the AR(1) model if the white noise (WN) process is non- Gaussian. Three estimators including the ordinary moment estimator and two other (robust) estimators are considered. The impacts of the deviation from normality of the WN process on those estimators in terms of bias, MSE and distribution via Monte-Carlo simulation are examined. The empirical distribution of those estimators when the errors are normal, t, Cauchy and exponential are studied. …
Two Parameter Modified Ratio Estimators With Two Auxiliary Variables For Estimation Of Finite Population Mean With Known Skewness, Kurtosis And Correlation Coefficient, Jambulingam Subramani, G Prabavathy
Two Parameter Modified Ratio Estimators With Two Auxiliary Variables For Estimation Of Finite Population Mean With Known Skewness, Kurtosis And Correlation Coefficient, Jambulingam Subramani, G Prabavathy
Journal of Modern Applied Statistical Methods
Consider the two parameter modified ratio estimators for the estimation of finite population mean using the skewness, kurtosis and correlation coefficient of two auxiliary variables. The efficiencies of the proposed modified ratio estimators are assessed with that of the simple random sampling without replacement (SRSWOR) sample mean and some of the existing ratio estimators in terms of mean squared errors. The entire above is explained with the help of certain natural populations available in the literature.
Change Point Estimation For Pareto Type-Ii Model, Gyan Prakash
Change Point Estimation For Pareto Type-Ii Model, Gyan Prakash
Journal of Modern Applied Statistical Methods
Some Bayes estimators of the change point for the Pareto Type-II model under right item failure-censoring scheme are proposed. The Bayes estimators are obtained here in two cases, the first is when one parameter is known and second when both parameters are considered as the random variable. The performances of the procedures are illustrated by simulation technique.
Comparison Of Three Calculation Methods For A Bayesian Inference Of Two Poisson Parameters, Yohei Kawasaki, Etsuo Miyaoka
Comparison Of Three Calculation Methods For A Bayesian Inference Of Two Poisson Parameters, Yohei Kawasaki, Etsuo Miyaoka
Journal of Modern Applied Statistical Methods
The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in medical literature. Kawasaki and Miyaoka (2012) proposed an index θ = P(λ1,post < λ2,post), where λ1,post and λ2,post denote Poisson parameters following posterior density. A new calculation method is proposed using MCMC and an approximate expression and exact expression for θ are compared.
Likelihood Ratio Type Test For Linear Failure Rate Distribution Vs. Exponential Distribution, R R. L. Kantam, M C. Priya, M S. Ravikumar
Likelihood Ratio Type Test For Linear Failure Rate Distribution Vs. Exponential Distribution, R R. L. Kantam, M C. Priya, M S. Ravikumar
Journal of Modern Applied Statistical Methods
The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and …
A Comparison Of Shape And Scale Estimators Of The Two-Parameter Weibull Distribution, Florence George
A Comparison Of Shape And Scale Estimators Of The Two-Parameter Weibull Distribution, Florence George
Journal of Modern Applied Statistical Methods
Weibull distributions are widely used in reliability and survival analysis. In this paper, different methods to estimate the shape and scale parameters of the two-parameter Weibull distribution have been reviewed and compared, based on the bias, mean square error and variance. Because a theoretical comparison is not possible, an extensive simulation study has been conducted to compare the performance of different estimators. Based on the simulation study it was observed that MLE consistently performs better than other methods.
An Alternative Test For The Equality Of Intraclass Correlation Coefficients Under Unequal Family Sizes For Several Populations, Madhusudan Bhandary, Koji Fujiwara
An Alternative Test For The Equality Of Intraclass Correlation Coefficients Under Unequal Family Sizes For Several Populations, Madhusudan Bhandary, Koji Fujiwara
Journal of Modern Applied Statistical Methods
An alternative test for the equality of several intraclass correlation coefficients under unequal family sizes based on several independent multinormal samples is proposed. It was found that the alternative test consistently and reliably produced results superior to those of Likelihood ratio test (LRT) proposed by Bhandary and Alam (2000) and Fmax test proposed by Bhandary and Fujiwara (2006) in terms of power for various combinations of intraclass correlation coefficient values and also the alternative test stays closer to the significance level under null hypothesis compared to the Likelihood ratio test and Fmax test. This alternative test is computationally …