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Journal Cover International Journal of Advanced Statistics and Probability
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  This is an Open Access Journal Open Access journal
     ISSN (Print) 2307-9045 - ISSN (Online) 2307-9045
     Published by Science Publishing Corporation Homepage  [12 journals]
  • Neyman’s causal model with stochastic potential outcomes:
           implications for the completely randomized design

    • Authors: Emil Scosyrev
      Abstract: In Neyman’s causal model (NCM), each subject participating in a two-arm randomized trial has a pair of potential outcomes – one outcome would be observed under treatment and another under control. In the stochastic version of NCM the two potential outcomes are viewed as possibly non-degenerate random variables with finite expectations and variances. The subject-level treatment effect is the expected outcome under treatment minus that under control, and the average treatment effect is the arithmetic mean of the subject-level effects. In the present paper properties of the ordinary “difference of means” estimator and its associated variance estimator are examined in the completely randomized design with stochastic potential outcomes. Estimation theory is developed under randomization distribution without commitment to any particular probability model for enrollment, because in real trials subjects are not enrolled by a sampling mechanism with known selection probabilities. It is shown that in this theoretical framework, the “difference of means” estimator is asymptotically normal and consistent for the average treatment effect in the study cohort, while its associated variance estimator is conservative, producing confidence intervals with at least nominal asymptotic coverage. The proofs are not trivial because in the randomization framework sample means under treatment and control are correlated random variables. Keywords: Causality; Clinical Trials; Internal Validity; Neyman’s Causal Model; Randomization-Based Inference; Stochastic Potential Outcomes.
      PubDate: 2014-07-15
      Issue No: Vol. 2 (2014)
  • Is there an absolutely continuous random variable with equal probability
           density and cumulative distribution functions in its support' Is it
           unique' What about in the discrete case'

    • Authors: Ernesto Veres-Ferrer, JoseM Pavia
      First page: 42
      Abstract: This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal. Keywords: Cumulative Distribution Function; Density Function; Elasticity; Mathematical Statistics; Reversed Hazard Rate.
      PubDate: 2014-06-02
      Issue No: Vol. 2 (2014)
  • Comparison of resampling method applied to censored data

    • Authors: Claude Arrabal, Karina Silva, Ricardo Rocha, Ricardo Nonaka, Silvana Meira
      First page: 48
      Abstract: This paper is about a comparison study among the performances of variance estimators of certain parameters, usingresampling techniques such as bootstrap and jackknife. The comparison will be made among several situations ofsimulated censored data, relating the observed values of estimates to real values. For real data, it will be consideredthe dataset Stanford heart transplant, analyzed by Cho et al. (2009) using the model of Cox regression (Cox, 1972)for adjustment. It is noted that the Jackknife residual is ecient to analyze inuential data points in the responsevariable. Keywords: bootstrap, Jackknife, simulation, Cox Regression Model, censored data.
      PubDate: 2014-06-05
      Issue No: Vol. 2 (2014)
  • Construction of second order slope rotatable designs under tri-diagonal
           correlated structure of errors using central composite designs

    • Authors: Rajyalakshmi kottapalli, B. Re. Victorbabu
      First page: 70
      Abstract: In this paper, second order slope rotatable design (SOSRD) under tri-diagonal correlated structure of errors using central composite designs (CCD) is suggested. Keywords: Response Surface Designs, Rotatable Designs, Slope Rotatable Designs, Second Order Slope Rotatable Designs (SOSRD), Tri-Diagonal Correlated Errors.
      PubDate: 2014-07-15
      Issue No: Vol. 2 (2014)
  • Estimation of the Parameters of the Bivariate Generalized Exponential
           Distribution using Accelerated Life Testing with Censoring Data

    • Authors: Salwa Asser, Mary Abd EL-Maseh
      First page: 77
      Abstract: In this paper, the estimation for the bivariate generalized exponential (BVGE) distribution under type-I censored with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The unknown parameters are estimated by the maximum likelihood approach and their approximate variance-covariance matrix is obtained. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the bivariate generalized exponential distribution. Keywords: Accelerated life testing, Bivariate generalized exponential distribution, Constant stress, Type-I censoring, Maximum likelihood estimation.
      PubDate: 2014-08-18
      Issue No: Vol. 2 (2014)
  • Semi-parametric mixed effects models for longitudinal data with
           applications in business and economics

    • Authors: Sunil Sapra
      First page: 84
      Abstract: Longitudinal data is becoming increasingly common in business, social sciences, and biological sciences due to the advantages it offers over cross-section data in modeling and incorporating heterogeneity among subjects and in being able to make causal inferences from observational data. Parametric models and methods are widely used for analyzing longitudinal data for continuous, discrete, and count data occurring in these disciplines. Some popular models are Gaussian, Logit, and Poisson fixed and random effects models. These models are unreliable in situations in which the link function is nonlinear and the form of nonlinearity is not known with certainty. This paper employs a semi-parametric extension of fixed and random effects models called generalized additive mixed models (GAMMs) to analyze several longitudinal data sets. These semi-parametric models are flexible and robust extensions of generalized linear models. Following Wood [19], the GAMMs are represented using penalized regression splines and estimated by penalized regression methods treating the penalized component of each smooth as a random effect term and the unpenalized component as a fixed effect term. The degree of smoothness for the unknown functions in the linear predictor part of the GAMM is estimated as the variance parameter of the term. Applications of GAMMs studied include analysis of anti-social behavior, decision to use a professional tax preparer, and analysis of patent data on manufacturing firms. For each application, several GAMMs are compared with their parametric counterparts. Keywords: Generalized Additive Mixed Models (GAMMS), Generalized Linear Mixed Models (GLMMS), Logit Models, Poisson Regression Models, Penalized Regression Splines.
      PubDate: 2014-09-25
      Issue No: Vol. 2 (2014)
  • Parameter estimation for multiple weibull populations under joint type-II

    • Authors: Samir Ashour, Osama Eraki
      First page: 102
      Abstract: In this paper, we introduce the maximum likelihood estimation for k Weibull populations under joint type II censored scheme and different special cases have been obtained.  The asymptotic variance covariance matrix and approximate confidence region based on the asymptotic normality of the maximum likelihood estimators have been obtained. A numerical example is considered to illustrate the proposed estimators. Keywords: Approximate Inference; Coverage Probabilities; Joint Type II Censored Scheme; Maximum Likelihood Estimation; Weibull Distribution.
      PubDate: 2014-09-26
      Issue No: Vol. 2 (2014)
  • Analysis of Generalized Exponential Distribution Under Adaptive Type-II
           Progressive Hybrid Censored Competing Risks Data

    • Authors: Samir Ashour, Mazen Nassar
      First page: 108
      Abstract: This paper presents estimates of the parameters based on adaptive type-II progressive hybrid censoring scheme (AT-II PHCS) in the presence of the competing risks model. We consider the competing risks have generalized exponential distributions (GED). The maximum likelihood method is used to derive point and asymptotic confidence intervals for the unknown parameters. The relative risks due to each cause of failure are investigated. A real data set is used to illustrate the theoretical results and to test the hypothesis that the causes of failure follow the generalized exponential distributions against the exponential distribution (ED). Keywords: Competing Risks; Adaptive Type-II Progressive Hybrid Censoring; Generalized Exponential Distribution; Maximum Likelihood Estimation.
      PubDate: 2014-09-30
      Issue No: Vol. 2 (2014)
  • Weibull-Bayesian analysis based on ranked set sampling

    • Authors: Amr Sadek, Fahad Alharbi
      First page: 114
      Abstract: Most of estimation methods reported in the literature are based on simple random sampling (SRS), which to certain extent is considerably less effective in estimating the parameters as compared to a new sampling technique, ranked set sampling (RSS) and its modifications. In this Paper we address the problem of Bayesian estimation of the parameters for Weibull distribution, based on ranked set sampling. Two loss functions have been studied: (i) the squared-error loss function as symmetric loss function, (ii) the linex loss function as asymmetric loss function. Different estimates are compared using simulations for illustrative purposes. Keywords: Bayes, Estimation, Loss function, priors, Ranked set sampling.
      PubDate: 2014-10-02
      Issue No: Vol. 2 (2014)
  • Certain effects of uncertain models

    • Authors: Brian Knaeble
      First page: 124
      Abstract: Statistical summaries of multiple regression analyses often state conclusions as if model uncertainty is of little concern. The error due to a mis-specified model, however, can be more significant in practice than the sampling error associated with commonly reported statistics. The true effect of an explanatory variable may be opposite that indicated by a fitted coefficient of a linear model, even if the model is well fit and the coefficient is deemed statistically significant. Here we study the sensitivity of the sign of a fitted coefficient to changes in the model structure. As a consequence of the principle of least squares, we show generally, that a set of covariates with a relatively weak coefficient of determination can not reverse the sign of a relatively strong fitted coefficient of a linear model that has been fit with a regression matrix having orthogonal columns. A consequence of the theory is a necessary condition for Simpson's paradox. Keywords: confounding, least squares, model uncertainty, regression, sensitivity analysis.
      PubDate: 2014-11-05
      Issue No: Vol. 2 (2014)
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