Outlier Detection in a Circular Regression Model Using COVRATIO Statistic

In this article, we model the relationship between two circular variables using the circular regression models, to be called JS circular regression model, which was proposed by Jammalamadaka and Sarma (1993). The model has many interesting properties and is sensitive enough to detect the occurrence of outliers. We focus our attention on the problem of identifying outliers in this model. In particular, we extend the use of the COVRATIO statistic, which has been successfully used in the linear case for the same purpose, to the JS circular regression model via a row deletion approach. Through simulation studies, the cut-off points for the new procedure are obtained and its power of performance is investigated. It is found that the performance improves when the resulting residuals have small variance and when the sample size gets larger. An example of the application of the procedure is presented using a real dataset.     

Efficiency estimation of type-I censored sample from the Weibull distribution based on sup-entropy

On the basis of Awad sup-entropy, the efficiency function for type-I censored sample from the Weibull distribution is numerically introduced. The properties of the derived efficiency are discussed. Furthermore, for a given efficiency, the termination time of the experiment, and the maximum likelihood estimates for the Weibull parameters, are proposed. Simulation results are tabulated and discussed. Censored and complete samples are compared for a wide range of the efficiency. The comparisons show the quality of the developed algorithms and the effectiveness of using censoring in estimating with the Weibull distribution.     

Semantic network representation of computer-mediated discussions: Conceptual facilitation form and knowledge acquisition

Prior research on computer-mediated discussions examined their effects on knowledge acquisition without considering the role of the discussion representation. In this study, we investigate and compare the effect of semantic network discussion representations on knowledge acquisition to that of the threaded representations featured in most traditional discussion forums. Furthermore, we identify, define and operationalize a new, i.e., conceptual facilitation (validation of the conceptual organization of the discussion), assessing its role in knowledge acquisition at different levels of restrictiveness. The empirical results of a field experiment indicate that semantic network discussion representations enable the acquisition of more complex and better-integrated knowledge structures than threaded discussion representations. Conceptual facilitation forms entailing different levels of restrictiveness are also found to play a significant role. As the level of conceptual facilitation restrictiveness decreases, knowledge acquisition improves. Our findings empirically demonstrate the importance of accounting for discussion representation as a contingency factor in explaining group discussion processes and outcomes. To practitioners, our study provides empirical evidence on the advantages of semantic networks over threaded representations as an alternative mode for computer-mediated discussion representations. We also suggest guidelines for the selection of appropriate conceptual facilitation for discussion forums intended for knowledge acquisition.     

Bayesian estimation of an AR(1) process with exponential white noise

The object of this paper is a Bayesian analysis of the autoregressive model X _t ?=?ρX _t?1?+?Y _t where 0?Y _t are independent random variables with an exponential distribution of parameter θ. Our study generalizes some results obtained by Turkmann (1990 Amaral Turkmann, M. A. (1990). Bayesian analysis of an autoregressive process with exponential white noise. Statistics, 4: 601–608.  [Google Scholar]). Our analysis is based on a more general non-informative prior which allows us to improve the estimators of ρ and θ.     

A New Test of Discordancy in Circular Data

In this article, we present an alternative test of discordancy in samples of univariate circular data. The new technique is based on the effect of existence of an outlier on the summation of circular distances of the point of interest to all other points. The percentage points are calculated and the performance is examined. We compare the performance of the test in detecting an outlier with other tests and show that the new approach performs relatively better than other known tests. As an illustration a practical example is presented.     

Generalized Linear Factor Models: A New Local EM Estimation Algorithm

In this article, a general approach to latent variable models based on an underlying generalized linear model (GLM) with factor analysis observation process is introduced. We call these models Generalized Linear Factor Models (GLFM). The observations are produced from a general model framework that involves observed and latent variables that are assumed to be distributed in the exponential family. More specifically, we concentrate on situations where the observed variables are both discretely measured (e.g., binomial, Poisson) and continuously distributed (e.g., gamma). The common latent factors are assumed to be independent with a standard multivariate normal distribution. Practical details of training such models with a new local expectation-maximization (EM) algorithm, which can be considered as a generalized EM-type algorithm, are also discussed. In conjunction with an approximated version of the Fisher score algorithm (FSA), we show how to calculate maximum likelihood estimates of the model parameters, and to yield inferences about the unobservable path of the common factors. The methodology is illustrated by an extensive Monte Carlo simulation study and the results show promising performance.     

Combined estimating function for random coefficient models with correlated errors

ABSTRACT

Estimating functionshave been shown to be convenient to study inference for non linear time series models. Recently, Thavaneswaran et al. (2012 Thavaneswaran, A., Liang, Y., Frank, J. (2012). Inference for random coefficient volatility models. Stat. Probab. Lett. 82(12):2086–2090.[Crossref], [Web of Science ®] , [Google Scholar]) used combined estimating functions to study inference for random coefficient autoregressive (RCA) models with generalized autoregressive heteroscedasticity errors. While most RCA modeling assumes that the random term and the error are independent, Chandra and Taniguchi (2001 Chandra, S.A., Taniguchi, M. (2001). Estimating functions for nonlinear time series models. Ann. Inst. Stat. Math 53(1):125–141.[Crossref], [Web of Science ®] , [Google Scholar]) studied inference for RCA models with correlated errors using linear estimating functions. In this paper, we derive the quadratic estimating functions for the joint estimation of the conditional mean, variance, and correlation parameters of the RCA models with correlated errors.     

A note on estimation and test for the rayleigh amplitude distribution

In an expository paper, Siddiqui (1962), presented and investigated the origin of the Rayleigh Power Distribution.He also discussed the problems of estimation and fitting the distribution to some numerical data. In this article we discuss two problems connected with the Rayleigh Amplitude Distribution (RAD). The first is an extension to the work done by Siddiqui on estimation, where the second is concerned with testing the equality of several Rayleigh Amplitude Distributions, and in this context we derive the asymptotic null distribution of the test criterion.     

Inverse Adaptive Cluster Sampling with Unequal Selection Probabilities: Case Studies on Crab Holes and Arsenic Pollution

Adaptive cluster sampling is an efficient method of estimating the parameters of rare and clustered populations. The method mimics how biologists would like to collect data in the field by targeting survey effort to localised areas where the rare population occurs. Another popular sampling design is inverse sampling. Inverse sampling was developed so as to be able to obtain a sample of rare events having a predetermined size. Ideally, in inverse sampling, the resultant sample set will be sufficiently large to ensure reliable estimation of population parameters. In an effort to combine the good properties of these two designs, adaptive cluster sampling and inverse sampling, we introduce inverse adaptive cluster sampling with unequal selection probabilities. We develop an unbiased estimator of the population total that is applicable to data obtained from such designs. We also develop numerical approximations to this estimator. The efficiency of the estimators that we introduce is investigated through simulation studies based on two real populations: crabs in Al Khor, Qatar and arsenic pollution in Kurdistan, Iran. The simulation results show that our estimators are efficient.