Showing papers in "Austrian Journal of Statistics in 2014"

The Transmuted Generalized Inverse Weibull Distribution

Abstract: A generalization of the generalized inverse Weibull distribution the so-called transmuted generalized inverse Weibull distribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking the generalized inverse Weibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the flexibility of the transmuted version versus the generalized inverse Weibull distribution.

The Beta Transmuted Weibull Distribution

Abstract: The paper introduces a beta transmuted Weibull distribution, which contains a number of distributions as special cases. The properties of the distribution are discussed and explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, and reliability. The distribution and moments of order statistics are also studied. Estimation of the model parameters by the method of maximum likelihood is discussed. The log beta transmuted Weibull model is introduced to analyze censored data. Finally, the usefulness of the new distribution in analyzing positive data is illustrated.

On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations

Abstract: We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency.

The Finite Population Bootstrap - From the Maximum Likelihood to the Horvitz-Thompson Approach

Abstract: The finite population bootstrap method is used as a computer-intensive alternative to estimate the sampling distribution of a sample statis-tic. The generation of a so-called “bootstrap population” is the necessarystep between the original sample drawn and the resamples needed to mimicthis distribution. The most important question for researchers to answer ishow to create an adequate bootstrap population, which may serve as a close-to-reality basis for the resampling process. In this paper, a review of someapproaches to answer this fundamental question is presented. Moreover, anapproach based on the idea behind the Horvitz-Thompson estimator allow-ing not only whole units in the bootstrap population but also parts of wholeunits is proposed. In a simulation study, this method is compared with a moreheuristic technique from the bootstrap literature.

On Outliers and Interventions in Count Time Series following GLMs

Abstract: We discuss the analysis of count time series following generalised linear models in the presence of outliers and intervention effects. Different modifications of such models are formulated which allow to incorporate, detect and to a certain degree distinguish extraordinary events (interventions) of different types in count time series retrospectively. An outlook on extensions to the problem of robust parameter estimation, identification of the model orders by robust estimation of autocorrelations and partial autocorrelations, and online surveillance by sequential testing for outlyingness is provided.

On the Exact Two-Sided Tolerance Intervals for Univariate Normal Distribution and Linear Regression

Abstract: Statistical tolerance intervals are another tool for making statistical inference on an unknown population. The tolerance interval is an interval estimator based on the results of a calibration experiment, which can be asserted with stated confidence level 1 − , for example 0.95, to contain at least a specified proportion 1 − , for example 0.99, of the items in the population under consideration. Typically, the limits of the tolerance intervals functionally depend on the tolerance factors. In contrast to other statistical intervals commonly used for statistical inference, the tolerance intervals are used relatively rarely. One reason is that the theoretical concept and computational complexity of the tolerance intervals is significantly more difficult than that of the standard confidence and prediction intervals. In this paper we present a brief overview of the theoretical background and approaches for computing the tolerance factors based on samples from one or several univariate normal (Gaussian) populations, as well as the tolerance factors for the non-simultaneous and simultaneous two-sided tolerance intervals for univariate linear regression. Such tolerance intervals are well motivated by their applicability in the multiple-use calibration problem and in construction of the calibration confidence intervals. For illustration, we present examples of computing selected tolerance factors by the implemented algorithm in MATLAB.

Estimation of Time Series Models via Robust Wavelet Variance

Abstract: A robust approach to the estimation of time series models is proposed. Taking from a new estimation method called the Generalized Method of Wavelet Moments (GMWM) which is an indirect method based on the Wavelet Variance (WV), we replace the classical estimator of the WV with a recently proposed robust M-estimator to obtain a robust version of the GMWM. The simulation results show that the proposed approach can be considered as a valid robust approach to the estimation of time series and state-space models.

Power-Law Random Graphs’ Robustness: Link Saving and Forest Fire Model

Abstract: We consider random graphs with node degrees drawn independently from a power- law distribution. By computer simulation we study two aspects of graph robustness: preserving graph connectivity and node saving in the forest fire model, considering two types of graph destruction: the removal of nodes with the highest degrees and equiprobable node extraction.

Multiple Imputation in the Austrian Household Survey on Housing Wealth

Abstract: This paper presents the multiple imputation model for the imputation of the missing values of the Austrian Household Survey on Housing Wealth 2008. It is based on Bayesian inference and on the fully conditional specification approach. Both theoretical framework and model specication are discussed in detail and, finally, some results about the performance of our imputations are presented.

Markov Chain of Conditional Order: Properties and Statistical Analysis

Abstract: The paper deals with finite Markov chain of conditional order, that is a special case of high-order Markov chain with a small number of parameters. Statistical estimators for parameters and statistical tests for parametric hypotheses are constructed and their properties are analyzed. Results of computer experiments on simulated and real data are presented.

Modelling Assumed Metric Paired Comparison Data - Application to Learning Related Emotions

Abstract: In this article we suggest a beta regression model that accounts for the degree of preference in paired comparisons measured on a bounded metric paired comparison scale. The beta distribution for bounded continuous random variables assumes values in the open unit interval (0,1). However, in practice we will observe paired comparison responses that lie within a fixed or arbitrary fixed interval [- a,a ] with known value of a . We therefore transform the observed responses into the interval (0,1) and assume that these transformed responses are each a realization of a random variable which follows a beta distribution. We propose a simple paired comparison regression model for beta distributed variables which allows us to model the mean of the transformed response using a linear predictor and a logit link function -- where the linear predictor is defined by the parameters of the logit-linear Bradley-Terry model. For illustration we applied the presented model to a data set obtained from a student survey of learning related emotions in mathematics.

Linguistic Summaries in Small Area Statistics

Abstract: Data collection in small area statistics also copes with missing values. In the municipal statistics we can recognize more or less similar municipalities and more or less dependent indicators. Therefore, an approach capable to process this uncertainty is desirable. Data produced in small area statistics are valuable source for users. Data dissemination which mimics human reasoning in searching and evaluation data could be a suitable solution. Thus, there is a space for improving both processes by linguistic summaries which are based on fuzzy logic. Finally, the paper discusses future research and development topics in this field.

Software Tools for Robust Analysis of High-Dimensional Data

Abstract: The present work discusses robust multivariate methods specifically designed for high dimensions. Their implementation in R is presented and their application is illustrated on examples. The first group are algorithms for outlier detection, already introduced elsewhere and implemented in other packages. The value added of the new package is that all methods follow the same design pattern and thus can use the same graphical and diagnostic tools. The next topic covered is sparse principal components including an object oriented interface to the standard method proposed by Zou, Hastie, and Tibshirani (2006) and the robust one proposed by Croux, Filzmoser, and Fritz (2013). Robust partial least squares (see Hubert and Vanden Branden 2003) as well as partial least squares for discriminant analysis conclude the scope of the new package.

Measurement of Continuous Quantities and their Statistical Evaluation

Abstract: Measurement results of continuous quantities are always more or less imprecise. This imprecision is different from errors. The most suitable mathematical model to describe imprecision is by special fuzzy subsets of the set of real numbers R, called characterizing functions. The statistical analysis of fuzzy measurement data is subject of this paper.

Macro-Integration for Solving Large Data Reconciliation Problems

Abstract: Macro-integration technique is a well established method for reconciliation of large, high-dimensional tables, especially applied to macroeconomic data at national statistical oces (NSO). This technique is mainly used when data obtained from dierent sources should be reconciled on a macro level. New areas of applications for this technique arise as new data sources become available to NSO's. Often these new data sources cannot be combined on a micro level, while macro integration could provide a solution for such problems. Yet, more research should be carried out to investigate if in such situations macro integration could indeed be applied. In this paper we propose two applications of macro-integration techniques in other domains than the traditional macro-economic applications. In particular: reconciliation of tables of a virtual census and reconciliation of monthly series of short term statistics gures with the quarterly gures of structural business statistics.

A Few Remarks on Robust Estimation of Power Spectra

Abstract: Various robust versions of the classical methods of power spectra estimation are considered. Their performance evaluation is studied in autoregressive models with contamination. It is found out that the best robust estimates of power spectra are based on robust highly efficient estimates of autocovariances. Several open problems for future research are formulated.

Estimation of the Domestic Transport Performance from the Consolidated European Road Freight Transport Data

Abstract: Transport statistics provide information about transport volume and performance on defined territories (e.g. for the European Union as a whole or for the individual member states) and are therefore necessary for political, economic and ecological decisions. Complying with the current European legal basis [1] the surveys for the modes of transport rail, aviation and inland waterways are performed according to the territoriality principle and hence the data on total transport volume is collected in each member state. Alone the road freight transport survey is based on the nationality principle, which means that only freight vehicles registered in the respective member state take part in the national surveys. Thus the single member states have no information about the total transport volume and performance on their own territory derived from road freight vehicles registered in other member states. In contrast the member states have information about the transport volume and performance provided by their freight vehicles in the other European countries. This situation implies a significant limitation of the usability of the results of the national road freight surveys as well as the usefulness of the modal split of the single modes of transport based solely on the national surveys. [1] Regulation (EC) No 91/2003 of the European Parliament and of the Council of 16 December 2002 on rail statistics, OJ No L14, 21.2.2003 p 1 - 15; Regulation (EC) No 437/2003 of the European Parliament and of the Council of 27 February 2003 on statistical returns in respect of the carriage of passengers, freight and mail by air; OJ No L 66, 11.3.2003 p 1 – 8; Regulation (EC) No 1365/2006 of the European Parliament and of the Council of 6 September 2006 on statistics of goods transport by inland waterways and repealing Council Directive 80/1119/EEC, OJ L No 264; 25.9.2006 p 1 – 11; Regulation (EU) No 70/2012 of the European Parliament and the Council of 18 January 2012 on statistical returns in respect of the carriage of goods by road (recast), OJ No L 32, 3.2.2012 p 1-18

Sensitivity Analysis for the Decomposition of Mixed Partitioned Multivariate Models into Two Seemingly Unrelated Submodels

Abstract: The paper is focused on the decomposition of mixed partitioned multivariate models into two seemingly unrelated submodels in order to obtain more efficient estimators. The multiresponses are independently normally distributed with the same covariance matrix. The partitioned multivariate model is considered either with, or without an intercept. The elimination transformation of the intercept that preserves the BLUEs of parameter matri- ces and the MINQUE of the variance components in multivariate models with and without an intercept is stated. Procedures on testing the decomposition of the partitioned model are presented. The properties of plug-in test statistics as functions of variance compo- nents are investigated by sensitivity analysis and insensitivity regions for the significance level are proposed. The insensitivity region is a safe region in the parameter space of the variance components where the approximation of the variance components can be used without any essential deterioration of the significance level of the plug-in test statistic. The behavior of plug-in test statistics and insensitivity regions is studied by simulations.

A Comparison of Bayesian Mixed Data Models for Austrian SILC data

Abstract: In many applications multidimensional outcome variables measured on different scales are of interest. In this paper we consider regression modelling of a bivariate response with a normal and a binary component. We use three different approaches to model dependence: a joint logit-normal model for the two responses, a factorization model with linear dependence and a a factorization model with flexible non-linear dependence. We apply these approaches to Austrian SILC data to analyse material deprivation and household income.

Family Generation Process from Administrative Data Sources and the Austrian Register-Based Census 2011

Abstract: For the Austrian register-based census we developed techniques to generate family statistics from administrative data sources. The approach is based on data of relationships and how to handle them -- in general, in a fixed household and in an imputation process. Therefore, we merged algebraic, graph theoretical and statistical tools to get a general framework.

Providing Data With High Utility And No Disclosure Risk For The Public and Researchers: An Evaluation By Advanced Statistical Disclosure Risk Methods

Abstract: The demand of data from surveys, registers or other data sets containing sensible information on people or enterprises have been increased significantly over the last years. However, before providing data to the public or to researchers, confidentiality has to be respected for any data set containing sensible individual information. Confidentiality can be achieved by applying statistical disclosure control (SDC) methods to the data. The research on SDC methods becomes more and more important in the last years because of an increase of the awareness on data privacy and because of the fact that more and more data are provided to the public or to researchers. However, for legal reasons this is only visible when the released data has (very) low disclosure risk. In this contribution existing disclosure risk methods are review and summarized. These methods are finally applied on a popular real-world data set - the Structural Earnings Survey (SES) of Austria. It is shown that the application of few selected anonymisation methods leads to well-protected anonymised data with high data utility and low information loss.

Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study

Abstract: The estimation of the population total $t_y,$ by using one or more auxiliary variables, and the population ratio $\theta_{xy}=t_y/t_x,$ $t_x$ is the population total for the auxiliary variable $X$, for a finite population are heavily discussed in the literature In this paper, the idea of estimation the finite population ratio $\theta_{xy}$ is extended to use the availability of auxiliary variable $Z$ in the study, such auxiliary variable is not used in the definition of the population ratio This idea may be supported by the fact that the variable $Z$ is highly correlated with the interest variable $Y$ than the correlation between the variables $X$ and $Y$ The availability of such auxiliary variable can be used to improve the precision of the estimation of the population ratio To our knowledge, this idea is not discussed in the literature The bias, variance and the mean squares error are given for our approach Simulation from real data set, the empirical relative bias and the empirical relative mean squares error are computed for our approach and different estimators proposed in the literature for estimating the population ratio $\theta_{xy}$ Analytically and the simulation results show that, by suitable choices, our approach gives negligible bias and has less mean squares error

Statistics and Probability at Secondary Schools in the Federal State of Salzburg: An Empirical Study

Abstract: Knowledge about the practical use of statistics and probability in today's mathematics instruction at secondary schools is vital in order to improve the academic education for future teachers. We have conducted an empirical study among school teachers to inform towards improved mathematics instruction and teacher preparation. The study provides a snapshot into the daily practice of instruction at school. Centered around the four following questions, the status of statistics and probability was examined. Where did the current mathematics teachers study? What relevance do statistics and probability have in school? Which contents are actually taught in class? What kind of continuing education would be desirable for teachers? The study population consisted of all teachers of mathematics at secondary schools in the federal state of Salzburg.

An Approach to Robustness Evaluation for Sequential Testing under Functional Distortions in L1-metric

Abstract: The problem of sensitivity analysis for the sequential probability ratio test under func- tional distortions of the observation probability distribution is considered. For the situa- tion where distorted densities of the log likelihood ratio statistic belong to e -neighborhoods of hypothetical centers in the L 1 -metric the least favorable distributions that maximize the conditional error probabilities are constructed. The instability coefficient is obtained to enable robustness evaluation for the sequential probability ratio test and its modification – trimmed sequential probability ratio test.