AStA Advances in Statistical Analysis

The variance of short-term systematic measurement errors for the difference of paired data is estimated. The difference of paired data is determined by subtracting the measurement results of two methods, which measure the same item only once without measurement repetition. The unbiased estimators for short-term systematic measurement error variances based on the one-way random effects model are not fit for practical purpose because they can be negative. The estimators, which are derived for balanced data as well as for unbalanced data, are always positive but biased. The basis of these positive estimators is the one-way random effects model. The biases, variances, and the mean squared errors of the positive estimators are derived as well as their estimators. The positive estimators are fit for practical purpose.

Latent variable models are widely used for jointly modeling of mixed data including nominal, ordinal, count and continuous data. In this paper, we consider a latent variable model for jointly modeling relationships between mixed binary, count and continuous variables with some observed covariates. We assume that, given a latent variable, mixed variables of interest are independent and count and continuous variables have Poisson distribution and normal distribution, respectively. As such data may be extracted from different subpopulations, consideration of an unobserved heterogeneity has to be taken into account. A mixture distribution is considered (for the distribution of the latent variable) which accounts the heterogeneity. The generalized EM algorithm which uses the Newton–Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. The standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. Analysis of the primary biliary cirrhosis data is presented as an application of the proposed model.

Mortality projections are of special interest in many applications. For example, they are essential in life insurances to determine the annual contributions of their members as well as for population predictions. Due to their importance, there exists a huge variety of mortality forecasting models from which to seek the best approach. In the demographic literature, statements about the quality of the various models are mostly based on empirical ex-post examinations of mortality data for very few populations. On the basis of such a small number of observations, it is impossible to precisely estimate statistical forecasting measures. We use Monte Carlo (MC) methods here to generate time trajectories of mortality tables, which form a more comprehensive basis for estimating the root-mean-square error (RMSE) of different mortality forecasts.

In this paper, case-deletion diagnostics in beta regression models are proposed. The diagnostics are based on the distance between the distributions of the maximum likelihood estimates of the model parameters resulting from the entire sample and after removing a sample case. Two metrics between probability distributions are considered: the Frèchet distance (Frèchet in Comptes Rendus hebdomadaires des seances de l’Academie des Sciences de Paris 244:689–692, 1957), and the Rao distance (Rao in Indian J Stat Ser A 9:246–291, 1949). Moreover, a jackknife-after-bootstrap transformation of the diagnostics is also proposed to make clear the decision about cases to be considered as influential. Artificial and real examples are included to illustrate the usefulness of the diagnostics and to compare them to others in the literature.

In this paper, we introduce a somewhat more general class of nonparametric estimators (delta-sequences estimators) for estimating an unknown regression operator from noisy data. The regressor is assumed to take values in an infinite-dimensional separable Banach space, when the response variable is a scalar. Under some general conditions, we establish the uniform almost-complete convergence with the rates of these estimators. Moreover, we give some particular cases of our results, which can also be considered as novel in the finite-dimensional setting. Moreover, after giving some examples of the impact of our results, we show how to use them in some statistical applications (prediction procedure and curve discrimination).

In this article, Figs. 1a, 2a-c, 9 and 11 should have appeared as shown below. The original article has been corrected.

Suppose that a finite population consists of N distinct units. Associated with the ith unit is a polychotomous response vector, d i , and a vector of auxiliary variable x i . The values x i ’s are known for the entire population but d i ’s are known only for the units selected in the sample. The problem is to estimate the finite population proportion vector P. One of the fundamental questions in finite population sampling is how to make use of the complete auxiliary information effectively at the estimation stage. In this article a predictive estimator is proposed which incorporates the auxiliary information at the estimation stage by invoking a superpopulation model. However, the use of such estimators is often criticized since the working superpopulation model may not be correct. To protect the predictive estimator from the possible model failure, a nonparametric regression model is considered in the superpopulation. The asymptotic properties of the proposed estimator are derived and also a bootstrap-based hybrid re-sampling method for estimating the variance of the proposed estimator is developed. Results of a simulation study are reported on the performances of the predictive estimator and its re-sampling-based variance estimator from the model-based viewpoint. Finally, a data survey related to the opinions of 686 individuals on the cause of addiction is used for an empirical study to investigate the performance of the nonparametric predictive estimator from the design-based viewpoint.

Generalized exponential distribution has been used quite effectively to model positively skewed lifetime data as an alternative to the well known Weibull or gamma distributions. In this paper we introduce an absolute continuous bivariate generalized exponential distribution by using a simple transformation from a well known bivariate exchangeable distribution. The marginal distributions of the proposed bivariate generalized exponential distributions are generalized exponential distributions. The joint probability density function and the joint cumulative distribution function can be expressed in closed forms. It is observed that the proposed bivariate distribution can be obtained using Clayton copula with generalized exponential distribution as marginals. We derive different properties of this new distribution. It is a five-parameter distribution, and the maximum likelihood estimators of the unknown parameters cannot be obtained in closed forms. We propose some alternative estimators, which can be obtained quite easily, and they can be used as initial guesses to compute the maximum likelihood estimates. One data set has been analyzed for illustrative purposes. Finally we propose some generalization of the proposed model.

Using rounded data to estimate moments and regression coefficients typically biases the estimates. We explore the bias-inducing effects of rounding, thereby reviewing widely dispersed and often half forgotten results in the literature. Under appropriate conditions, these effects can be approximately rectified by versions of Sheppard’s correction formula. We discuss the conditions under which these approximations are valid and also investigate the efficiency loss caused by rounding. The rounding error, which corresponds to the measurement error of a measurement error model, has a marginal distribution, which can be approximated by the uniform distribution, but is not independent of the true value. In order to take account of rounding preferences (heaping), we generalize the concept of simple rounding to that of asymmetric rounding and consider its effect on the mean and variance of a distribution.