A new log-location regression model: estimation,influence diagnostics and residual analysis

We introduce a log-linear regression model based on the odd log-logistic generalized half-normal distribution [7 G.M. Cordeiro, M. Alizadeh, R.R. Pescim, and E.M.M. Ortega, The odd log-logistic generalized half-normal lifetime distribution: Properties and applications, Comm. Statist. Theory Methods (2015), accepted for publication. [Google Scholar]]. Some of its structural properties including explicit expressions for the density function, quantile and generating functions and ordinary moments are derived. We estimate the model parameters by the maximum likelihood method. For different parameter settings, proportion of censoring and sample size, some simulations are performed to investigate the behavior of the estimators. We derive the appropriate matrices for assessing local influence diagnostics on the parameter estimates under different perturbation schemes. We also define the martingale and modified deviance residuals to detect outliers and evaluate the model assumptions. In addition, we demonstrate that the extended regression model can be very useful in the analysis of real data and provide more realistic fits than other special regression models. The potentiality of the new regression model is illustrated by means of a real data set.     

Model selection criteria in beta regression with varying dispersion

We address the issue of model selection in beta regressions with varying dispersion. The model consists of two submodels, namely: for the mean and for the dispersion. Our focus is on the selection of the covariates for each submodel. Our Monte Carlo evidence reveals that the joint selection of covariates for the two submodels is not accurate in finite samples. We introduce two new model selection criteria that explicitly account for varying dispersion and propose a fast two step model selection scheme which is considerably more accurate and is computationally less costly than usual joint model selection. Monte Carlo evidence is presented and discussed. We also present the results of an empirical application.     

Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts

The adaptive exponentially weighted moving average (AEWMA) control chart is a smooth combination of the Shewhart and exponentially weighted moving average (EWMA) control charts. This chart was proposed by Cappizzi and Masarotto (2003) to achieve a reasonable performance for both small and large shifts. Cappizzi and Masarotto (2003) used a pair of shifts in designing their control chart. In this study, however, the process mean shift is considered as a random variable with a certain probability distribution and the AEWMA control chart is optimized for a wide range of mean shifts according to that probability distribution and not just for a pair of shifts. Using the Markov chain technique, the results show that the new optimization design can improve the performance of the AEWMA control chart from an overall point of view relative to the various designs presented by Cappizzi and Masarotto (2003). Optimal design parameters that achieve the desired in-control average run length (ARL) are computed in several cases and formulas used to find approximately their values are given. Using these formulas, the practitioner can compute the optimal design parameters corresponding to any desired in-control ARL without the need to apply the optimization procedure. The results obtained by these formulas are very promising and would particularly facilitate the design of the AEWMA control chart for any in-control ARL value.     

A new nonlinear asymmetric cointegration approach using error correction models

In this article, two new powerful tests for cointegration are proposed. The general idea is based on an intuitively appealing extension of the traditional, rather restrictive cointegration concept. In this article, we allow for a nonlinear, but most importantly a different, asymmetric convergence process to account for negative and positive changes in our cointegration approach. Using Monte Carlo simulations we verify, that the estimated size of the first test depends on the unknown value of a signal-to-noise ratio q. However, our second test—which is based on the original ideas of Kanioura and Turner—is more successful and robust in the sense that it works in all of the different evaluated situations. Furthermore it is shown to be more powerful than the traditional residual based Enders and Siklos method. The new optimal test is also applied in an empirical example in order to test for potential nonlinear asymmetric price transmission effects on the Swedish power market. We find that there is a higher propensity for power retailers to rapidly and systematically increase their retail electricity prices subsequent to increases in Nordpool's wholesale prices, than there is for them to reduce their prices subsequent to a drop in wholesale spot prices.     

Monitoring the coefficient of variation using a variable sample size and sampling interval control chart

This article proposes a CV chart by using the variable sample size and sampling interval (VSSI) feature to improve the performance of the basic CV chart, for detecting small and moderate shifts in the CV. The proposed VSSI CV chart is designed by allowing the sample size and the sampling interval to vary. The VSSI CV chart's statistical performance is measured by using the average time to signal (ATS) and expected average time to signal (EATS) criteria and is compared with that of existing CV charts. The Markov chain approach is employed in the design of the chart.     

Markov regime switching in mean and in fractional integration parameter

We propose a specific general Markov-regime switching estimation both in the long memory parameter d and the mean of a time series. We employ Viterbi algorithm that combines the Viterbi procedures in two state Markov-switching parameter estimation. It is well-known that existence of mean break and long memory in time series can be easily confused with each other in most cases. Thus, we aim at observing the deviation and interaction of mean and d estimates for different cases. A Monte Carlo experiment reveals that the finite sample performance of the proposed algorithm for a simple mixture model of Markov-switching mean and d changes with respect to the fractional integrating parameters and the mean values for the two regimes.     

Bootstrap approach to test the homogeneity of order restricted mean vectors when the covariance matrices are unknown

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are unknown, arbitrary positive definite and unequal are considered. This problem of testing has been studied to some extent, for example, by Kulatunga and Sasabuchi (1984 Kulatunga, D. D. S., Sasabuchi, S. (1984). A test of homogeneity of mean vectors against multivariate isotonic alternatives. Mem Fac Sci, Kyushu Univ Ser A Mathemat 38:151–161. [Google Scholar]) when the covariance matrices are known and also Sasabuchi et al. (2003 Sasabuchi, S., Tanaka, K., Tsukamodo, T. (2003). Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Annals of Statistics. 31(5):1517–1536.[Web of Science ®] , [Google Scholar]) and Sasabuchi (2007 Sasabuchi, S. (2007). More powerful tests for homogeneity of multivariate normal mean vectors under an order restriction. Sankhya 69(4):700–716. [Google Scholar]) when the covariance matrices are unknown but common. In this paper, a test statistic is proposed and because of the main advantage of the bootstrap test is that it avoids the derivation of the complex null distribution analytically, a bootstrap test statistic is derived and since the proposed test statistic is location invariance the bootstrap p-value defined logical and some steps are presented to estimate it. Our numerical studies via Monte Carlo simulation show that the proposed bootstrap test can correctly control the type I error rates. The power of the test for some of the p-dimensional normal distributions is computed by Monte Carlo simulation. Also, the null distribution of test statistic is estimated using kernel density. Finally, the bootstrap test is illustrated using a real data.     

The inverse power Lindley distribution

Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, two generalizations of the Lindley distribution were proposed in the literature: the power Lindley distribution and the inverse Lindley distribution. In this article, a distribution is obtained from these two generalizations and named as inverse power Lindley distribution. Some properties of this distribution and study of the behavior of maximum likelihood estimators are presented and discussed. It is also applied considering two real datasets and compared with the fits obtained for already-known distributions. When applied, the inverse power Lindley distribution was found to be a good alternative for modeling survival data.     

Riemann manifold Langevin methods on stochastic volatility estimation

In this article, we perform Bayesian estimation of stochastic volatility models with heavy tail distributions using Metropolis adjusted Langevin (MALA) and Riemman manifold Langevin (MMALA) methods. We provide analytical expressions for the application of these methods, assess the performance of these methodologies in simulated data, and illustrate their use on two financial time series datasets.     

On fiducial generators

Fiducial inference has been gaining presence recently and it is the intention of the present article to look at the notion of fiducial generators; meaning procedures to simulate parameter values that in some sense correspond to simulations from some implicit fiducial distribution. It is well known that when the distribution has group structure, stemming from the natural pivotal associated, a fiducial may be obtained. It is in the non group distributions that there appears to be still room for finding a fiducial distribution. Recently some general procedures have been proposed for dealing with generalized fiducials, but these depend on certain choices for a structural equation or a fiducial equation, as in Hannig (2009 Hannig, J. (2009). On generalized fiducial inference. Stat. Sin. 19:491–544.[Web of Science ®] , [Google Scholar]) or Taraldsen and Lindqvist (2013 Taraldsen, G., Lindqvist, B.H. (2013). Fiducial theory and optimal inference. Ann. Stat. 41(1):323–341.[Crossref], [Web of Science ®] , [Google Scholar]), respectively. A brief presentation is made of an earlier approach to fiducial inference for multivariate parameters, as in Brillinger (1962 Brillinger, D.R. (1962). Examples bearing on the definition of fiducial probability with a bibliography. Ann. Math. Stat. 33(4):1349–1355.[Crossref] , [Google Scholar]), and the implied fiducial generator introduced in Engen and Lillegård (1997 Engen, S., Lillegård, M. (1997). Stochastic simulation conditioned on sufficient statistics. Biometrika 84(1):235–240.[Crossref], [Web of Science ®] , [Google Scholar]), trying to connect them. Three interesting non group distributions are seen; two of them, the truncated exponential and the two-parameter gamma, already reported in literature. A third non group distribution is analyzed; the inverse Gaussian, connecting the fiducial that results following Brillinger (1962 Brillinger, D.R. (1962). Examples bearing on the definition of fiducial probability with a bibliography. Ann. Math. Stat. 33(4):1349–1355.[Crossref] , [Google Scholar]), with a result pertaining confidence limits for the shape parameter in Hsieh (1990 Hsieh, H.K. (1990). Inferences on the coefficient of variation of an inverse-Gaussian distribution. Commun. Stat. - Theory Methods 19(5):1589–1605.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). In the three cases, comparisons are made with the Bayesian posteriors that have been known to be close numerically. Some discussion is made on the issue of singularities of the fiducial density and its connection with densities that do not integrate to unity. As to the case of discrete observables, some comments are made for the Bernoulli distribution, only.