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## Verteilungen

### Statistische Datenanalyse (2004-01-01): 7-28 , January 01, 2004

### Zusammenfassung

Als erster Schritt der statistischen Datenanalyse sollten die erhobenen Daten geeignet aufbereitet werden, sodass über eine tabellarische bzw. grafische Darstellung ein vertiefter Einblick in den Informationsgehalt der Daten möglich ist.

## Local Influence Analysis for Mixture of Structural Equation Models

### Journal of Classification (2004-03-01) 21: 111-137 , March 01, 2004

## Introduction

### Data Analysis Using the Method of Least Squares (2006-01-01): 1-29 , January 01, 2006

## Statistics and Measurement in the Earth Sciences

### Statistical Methods for the Earth Scientist (1974-01-01): 1-6 , January 01, 1974

The word statistics was first used in 1770, but with a rather different meaning from that used today. One chapter of Hooper’s *The Elements of Universal Erudition* published in 1770 is entitled ‘Statistics’ and deals with ‘the science that teaches us what is the political arrangement of all the modern States of the known world’ (Yule and Kendall, 1953). In the early decades of the nineteenth century the change to ‘statistics’ representing the characters of a State by numerical methods was taking place. Only by the end of the century were ‘statistics’ the summary figures used to describe and compare the properties of a set of observations. At about this time the theoretical basis of the science of statistics was being laid, and today we find the ideas of statistics on a firm basis and applied to the collection, summary and analysis of all types of data.

## A Thick Modeling Approach to Multivariate Volatility Prediction

### Advances in Latent Variables (2015-01-01) , January 01, 2015

This paper proposes a modified approach to the combination of forecasts from multivariate volatility models where the combination is performed over a restricted subset including only the best performing models. Such a subset is identified over a rolling window by means of the Model Confidence Set (MCS) approach. The analysis is performed using different combination schemes, both linear and non linear, and considering different loss functions for the evaluation of the forecasting performance. An application to a vast dimensional portfolio of 50 NYSE stocks shows that (a) in non-extreme volatility periods the use of forecast combinations allows to improve over the predictive accuracy of the single candidate models (b) performing the combination over the subset of most accurate models does not significantly reduce the accuracy of the combined predictor.

## The Utility of the Hui-Walter Paradigm for the Evaluation of Diagnostic Test in the Analysis of Social Science Data

### Diagnosis and Prediction (1999-01-01) 114: 7-29 , January 01, 1999

Just as in medical research, social scientists are concerned with the correct classification of individuals into well defined categories. Many economic policy decisions rely on the unemployment rate and related labor statistics. As the unemployment rate is the ratio of the estimated number of unemployed persons to the total labor force, misclassification of survey respondents may lead to an under or over estimate of it. Thus, estimating the accuracy of the original interview is quite important and the Census Bureau conducts a special reinterview study of about 20,000 respondents per year to monitor their error rates. In law, a large body of research (Hans and Vidmar; 1991, Blank and Rosenthal; 1991) has raised questions about how well the jury functions. The basic problem can be placed in the classification frame work. How well does the current system perform in correctly determining that a guilty party is found guilty and in not convicting an individual who should be acquitted ? This article reports some exploratory work we have carried out on extending and modifying the Hui-Walter methodology for evaluating the accuracy of diagnostic tests (see Vianna, 1995, for related work) to enable us to estimate the accuracy of the labor force data and to reanalyze a classic study (Kalven and Zeisel, 1966) of judge-jury agreements to estimate the accuracy of jury verdicts.

## Maximum likelihood estimation of Gaussian mixture models without matrix operations

### Advances in Data Analysis and Classification (2015-12-01) 9: 371-394 , December 01, 2015

The Gaussian mixture model (GMM) is a popular tool for multivariate analysis, in particular, cluster analysis. The expectation–maximization (EM) algorithm is generally used to perform maximum likelihood (ML) estimation for GMMs due to the M-step existing in closed form and its desirable numerical properties, such as monotonicity. However, the EM algorithm has been criticized as being slow to converge and thus computationally expensive in some situations. In this article, we introduce the linear regression characterization (LRC) of the GMM. We show that the parameters of an LRC of the GMM can be mapped back to the natural parameters, and that a minorization–maximization (MM) algorithm can be constructed, which retains the desirable numerical properties of the EM algorithm, without the use of matrix operations. We prove that the ML estimators of the LRC parameters are consistent and asymptotically normal, like their natural counterparts. Furthermore, we show that the LRC allows for simple handling of singularities in the ML estimation of GMMs. Using numerical simulations in the R programming environment, we then demonstrate that the MM algorithm can be faster than the EM algorithm in various large data situations, where sample sizes range in the tens to hundreds of thousands and for estimating models with up to 16 mixture components on multivariate data with up to 16 variables.

## A new instrumental variable estimation for diffusion processes

### Annals of the Institute of Statistical Mathematics (2005-12-01) 57: 733-745 , December 01, 2005

We consider the problem of parametric inference from continuous sample paths of the diffusion processes {*x(t)}* generated by the system of possibly nonstationary and/or nonlinear Ito stochastic differential equations. We propose a new instrumental variable estimator of the parameter whose pivotal statistic has a Gaussian distribution for all possible values of parameter. The new estimator enables us to construct exact level-α confidence intervals and tests for the parameter in the possibly non-stationary and/or nonlinear diffusion processes. Applications to several non-stationary and/or nonlinear diffusion processes are considered as examples.

## Multivariate Ranks-Based Concordance Indexes

### Advanced Statistical Methods for the Analysis of Large Data-Sets (2012-01-01) , January 01, 2012

The theoretical contributions to a “good” taxation have put the attention on the relations between the efficiency and the vertical equity without considering the “horizontal equity” notion: only recently, measures connected to equity (iniquity) of a taxation have been introduced in literature. The taxation problem is limited to the study of two quantitative characters: however the concordance problem can be extended in a more general context as we present in the following sections. In particular, the aim of this contribution consists in defining concordance indexes, as dependence measures, in a multivariate context. For this reason a *k*-variate (*k* > 2) concordance index is provided recurring to statistical tools such as ranks-based approach and multiple linear regression function. All the theoretical topics involved are shown through a practical example.

## Statistical Process Control Charts as a Tool for Analyzing Big Data

### Big and Complex Data Analysis (2017-01-01): 123-138 , January 01, 2017

Big data often take the form of data streams with observations of certain processes collected sequentially over time. Among many different purposes, one common task to collect and analyze big data is to monitor the longitudinal performance/status of the related processes. To this end, statistical process control (SPC) charts could be a useful tool, although conventional SPC charts need to be modified properly in some cases. In this paper, we introduce some basic SPC charts and some of their modifications, and describe how these charts can be used for monitoring different types of processes. Among many potential applications, dynamic disease screening and profile/image monitoring will be discussed in some detail.