The Co-Integrated Vector Autoregression with Errors–in–Variables

The co-integrated vector autoregression is extended to allow variables to be observed with classical measurement errors (ME). For estimation, the model is parametrized as a time invariant state-space form, and an accelerated expectation-maximization algorithm is derived. A simulation study shows that (i) the finite-sample properties of the maximum likelihood (ML) estimates and reduced rank test statistics are excellent (ii) neglected measurement errors will generally distort unit root inference due to a moving average component in the residuals, and (iii) the moving average component may–in principle–be approximated by a long autoregression, but a pure autoregression cannot identify the autoregressive structure of the latent process, and the adjustment coefficients are estimated with a substantial asymptotic bias. An application to the zero-coupon yield-curve is given.     

The Weibull–Pareto Composite Family with Applications to the Analysis of Unimodal Failure Rate Data

The Weibull distribution is composited with Pareto model to obtain a flexible, reliable long-tailed parametric distribution for modeling unimodal failure rate data. The hazard function of the composite family accommodates decreasing and unimodal failure rates, which are separated by the boundary line of the space of shape parameter, gamma, when it equals to a known constant. The least square and maximum likelihood parameter estimation techniques are discussed. The advantages of using the proposed family are demonstrated and compared by illustrating well-known examples: guinea pigs survival time data, head and neck cancer data, and nasopharynx cancer survival data.     

The efficiency of Efron's “Bootstrap” Approach Applied to Error Rate Estimation in Discriminant Analysis

The “bootstrap” approach of Efron is considered in its application to the estimation of error rates in discriminant analysis. Its efficiency relative to parametric estimation is investigated by simulation for Fisher's linear discriminant function in the context of two multivariate normal populations with a common covariance matrix.     

The Secular and Cyclical Behavior of Real GDP in 19 OECD Countries, 1957–1983

Log per capita real gross domestic product is modeled as a third-order autoregression with a pair of complex roots whose amplitude is smaller than the amplitude of the real root. The behavior of this terms series is interpreted in terms of these two amplitudes, the periodicity of the complex roots, and the standard deviation of the disturbance. Restrictions are evaluated and inference is conducted using the likelihood principle, applying Monte Carlo integration with importance sampling. These Bayesian procedures efficiently cope with restrictions that are awkward taking a classical approach. We find very little difference in the amplitudes of real roots between countries and of complex roots relative to within-country uncertainty. There are some substantial differences in the periodicities of complex roots, and the greatest differences between countries are found in the standard deviation of the disturbance.     

The Bernstein–von Mises theorem in semiparametric competing risks models

Semiparametric Bayesian models are nowadays a popular tool in event history analysis. An important area of research concerns the investigation of frequentist properties of posterior inference. In this paper, we propose novel semiparametric Bayesian models for the analysis of competing risks data and investigate the Bernstein–von Mises theorem for differentiable functionals of model parameters. The model is specified by expressing the cause-specific hazard as the product of the conditional probability of a failure type and the overall hazard rate. We take the conditional probability as a smooth function of time and leave the cumulative overall hazard unspecified. A prior distribution is defined on the joint parameter space, which includes a beta process prior for the cumulative overall hazard. We first develop the large-sample properties of maximum likelihood estimators by giving simple sufficient conditions for them to hold. Then, we show that, under the chosen priors, the posterior distribution for any differentiable functional of interest is asymptotically equivalent to the sampling distribution derived from maximum likelihood estimation. A simulation study is provided to illustrate the coverage properties of credible intervals on cumulative incidence functions.     

The Volume of Transactions and the Circulation of Money in the United States, 1950–1979

In the identity of exchange I distinguish between currency and bank payments on one side and several types of transactions and the transfer of idle money on the other. An attempt is made to measure these variables, with varying success. On the payments side I argue that currency velocity is constant (and low) and that the vast rise of bank money velocity is largely due to increased short-term investment of idle funds. The results suggest an upward shift in the level of transactions in 1968–1972, which I attribute to changes in the international role of the dollar.     

The Generalized Birnbaum–Saunders Distribution and Its Theory,Methodology, and Application

In this paper, we discuss the class of generalized Birnbaum–Saunders distributions, which is a very flexible family suitable for modeling lifetime data as it allows for different degrees of kurtosis and asymmetry and unimodality as well as bimodality. We describe the theoretical developments on this model including properties, transformations and related distributions, lifetime analysis, and shape analysis. We also discuss methods of inference based on uncensored and censored data, diagnostics methods, goodness-of-fit tests, and random number generation algorithms for the generalized Birnbaum–Saunders model. Finally, we present some illustrative examples and show that this distribution fits the data better than the classical Birnbaum–Saunders model.     

Rate of convergence for asymptotic variance of the Horvitz–Thompson estimator

Drawing distinct units without replacement and with unequal probabilities from a population is a problem often considered in the literature (e.g. Hanif and Brewer, 1980, Int. Statist. Rev. 48, 317–355). In such a case, the sample mean is a biased estimator of the population mean. For this reason, we use the unbiased Horvitz–Thompson estimator (1951). In this work, we focus our interest on the variance of this estimator. The variance is cumbersome to compute because it requires the calculation of a large number of second-order inclusion probabilities. It would be helpful to use an approximation that does not need heavy calculations. The Hájek (1964) variance approximation provides this advantage as it is free of second-order inclusion probabilities. Hájek (1964) proved that this approximation is valid under restrictive conditions that are usually not fulfilled in practice. In this paper, we give more general conditions and we show that this approximation remains acceptable for most practical problems.     

The Distribution of the Kolmogorov–Smirnov,Cramer–von Mises,and Anderson–Darling Test Statistics for Exponential Populations with Estimated Parameters

This article presents a derivation of the distribution of the Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–Darling test statistics in the case of exponential sampling when the parameters are unknown and estimated from sample data for small sample sizes via maximum likelihood.     

The Multistep Beveridge–Nelson Decomposition

The Beveridge–Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The article introduces the multistep Beveridge–Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge–Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge–Nelson trend is more efficient than the standard one in the presence of model misspecification, and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.     

The Balakrishnan skew–normal density

We consider a generalization of the Azzalini skew–normal distribution. We denote this distribution by SNB _n (λ). Some properties of SNB _n (λ) are studied. Its moment generating function is derived, and the bivariate case of SNB _n (λ) is introduced. Finally, we illustrate a numerical example and we present an application for order statistics.     

Trend,Growth Rate,and Change Point Analysis—A Data Driven Approach

A data-driven technique is proposed to estimate the trend and relative growth rate of time series data. The method is based on the local linear regression smoother and the only assumption about the form of the trend and growth rate function is that they are smooth functions of time. We also extended the method for handling sudden shifts or changes in the trend or growth rate functions by adding dummy variables for the jumps. Simulation studies are carried out to see the performance of the proposed procedure. The method is applied to study the trend and growth rate of wheat production in India from 1951–2005.     

The exponential–Weibull lifetime distribution

In this paper, we propose a new three-parameter model called the exponential–Weibull distribution, which includes as special models some widely known lifetime distributions. Some mathematical properties of the proposed distribution are investigated. We derive four explicit expressions for the generalized ordinary moments and a general formula for the incomplete moments based on infinite sums of Meijer's G functions. We also obtain explicit expressions for the generating function and mean deviations. We estimate the model parameters by maximum likelihood and determine the observed information matrix. Some simulations are run to assess the performance of the maximum likelihood estimators. The flexibility of the new distribution is illustrated by means of an application to real data.     

The admissible minimax estimator in Gauss–Markov model under a balanced loss function

In this paper, we investigate the admissible minimax estimator (AME) of regression coefficient in Gauss–Markov model under a balanced loss function. In the class of homogeneous linear estimators, we obtain the AME under two occasions, respectively. We also prove that the AME is a shrinkage estimator of the best linear unbiased estimator (BLUE). Furthermore, we prove that the AME dominates the BLUE under certain conditions.     

The generalized T Birnbaum–Saunders family

In this work, we generalize the Birnbaum–Saunders distribution using the generalized t distribution alternatively to the normal distribution. The newly defined family is positively skewed and contains distributions with different kurtosis and skewness. We study its properties and special cases and demonstrate its use on some real data sets considering the maximum-likelihood estimation procedure.