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## Prediction model-based kernel density estimation when group membership is subject to missing

### AStA Advances in Statistical Analysis (2017-07-01) 101: 267-288 , July 01, 2017

The density function is a fundamental concept in data analysis. When a population consists of heterogeneous subjects, it is often of great interest to estimate the density functions of the subpopulations. Nonparametric methods such as kernel smoothing estimates may be applied to each subpopulation to estimate the density functions if there are no missing values. In situations where the membership for a subpopulation is missing, kernel smoothing estimates using only subjects with membership available are valid only under missing complete at random (MCAR). In this paper, we propose new kernel smoothing methods for density function estimates by applying prediction models of the membership under the missing at random (MAR) assumption. The asymptotic properties of the new estimates are developed, and simulation studies and a real study in mental health are used to illustrate the performance of the new estimates.

## G. Molenberghs and G. Verbeke: Models for Discrete Longitudinal Data

### AStA Advances in Statistical Analysis (2007-08-01) 91: 223-224 , August 01, 2007

## Recent developments in life and social science applications of capture–recapture methods

### AStA Advances in Statistical Analysis (2009-03-01) 93: 1-3 , March 01, 2009

## Longitudinal dynamic analyses of cognition in the health and retirement study panel

### AStA Advances in Statistical Analysis (2011-12-01) 95: 453-480 , December 01, 2011

The purpose of this paper is to highlight some classic issues in the measurement of change and to show how contemporary solutions can be used to deal with some of these issues. Five classic issues will be raised here: (1) Separating individual changes from group differences; (2) options for incomplete longitudinal data over time, (3) options for nonlinear changes over time; (4) measurement invariance in studies of changes over time; and (5) new opportunities for modeling dynamic changes. For each issue we will describe the problem, and then review some contemporary solutions to these problems base on Structural Equation Models (SEM). We will fit these SEM to using existing panel data from the Health & Retirement Study (HRS) cognitive variables. This is not intended as an overly technical treatment, so only a few basic equations are presented, examples will be displayed graphically, and more complete references to the contemporary solutions will be given throughout.

## Goodness-of-fit testing for the marginal distribution of regime-switching models with an application to electricity spot prices

### AStA Advances in Statistical Analysis (2013-07-01) 97: 239-270 , July 01, 2013

This paper complements a recently published study (Janczura and Weron in AStA-Adv Stat Anal 96(3):385–407, 2012) on efficient estimation of Markov regime-switching models. Here, we propose a new goodness-of-fit testing scheme for the marginal distribution of such models. We consider models with an observable (like threshold autoregressions) as well as a latent state process (like Markov regime-switching). The test is based on the Kolmogorov–Smirnov supremum-distance statistic and the concept of the weighted empirical distribution function. The motivation for this research comes from a recent stream of literature in energy economics concerning electricity spot price models. While the existence of distinct regimes in such data is generally unquestionable (due to the supply stack structure), the actual goodness-of-fit of the models requires statistical validation. We illustrate the proposed scheme by testing whether commonly used Markov regime-switching models fit deseasonalized electricity prices from the NEPOOL (US) day-ahead market.

## A formal framework for hedonic elementary price indices

### AStA Advances in Statistical Analysis (2017-02-22): 1-27 , February 22, 2017

Hedonic methods are considered state of the art for handling quality changes when compiling consumer price indices. The present article proposes first a mathematical description of characteristics and of elementary aggregates. In a following step, a hedonic econometric model is formulated and hedonic elementary population indices are defined. We emphasise that population indices are unobservable economic parameters that need to be estimated by suitable sample indices. It is shown that within the framework developed here, many of the hedonic index formulae used in practice are identified as sample versions corresponding to particular hedonic elementary population indices. The article closes with an empirical part on quarterly housing data where the considered hedonic indices are estimated along with their bootstrapped confidence intervals. It is shown that the computed confidence intervals together with the results from theory suggest a particular answer to the price index problem.

## The power function of conditional tests of the Rasch model

### AStA Advances in Statistical Analysis (2015-07-01) 99: 367-378 , July 01, 2015

In this paper, a general expression of the power function of conditional or pseudo-exact tests of the Rasch model is derived. It allows the determination of the power of conditional tests against various alternative hypotheses. A number of relevant examples frequently occurring in practice are discussed. With respect to computations, a Monte Carlo approach is suggested enabling the approximation of the exact power in applications.

## Illuminate the unknown: evaluation of imputation procedures based on the SAVE survey

### AStA Advances in Statistical Analysis (2013-01-01) 97: 49-76 , January 01, 2013

Questions about monetary variables (such as income, wealth or savings) are key components of questionnaires on household finances. However, missing information on such sensitive topics is a well-known phenomenon which can seriously bias any inference based only on complete-case analysis. Many imputation techniques have been developed and implemented in several surveys. Using the German SAVE data, a new estimation technique is necessary to overcome the upward bias of monetary variables caused by the initially implemented imputation procedure. The upward bias is the result of adding random draws to the implausible negative values predicted by OLS regressions until all values are positive. To overcome this problem the logarithm of the dependent variable is taken and the predicted values are retransformed to the original scale by Duan’s smearing estimate. This paper evaluates the two different techniques for the imputation of monetary variables implementing a simulation study, where a random pattern of missingness is imposed on the observed values of the variables of interest. A Monte-Carlo simulation based on the observed data shows the superiority of the newly implemented smearing estimate to construct the missing data structure. All waves are consistently imputed using the new method.

## Inference on finite population categorical response: nonparametric regression-based predictive approach

### AStA Advances in Statistical Analysis (2012-01-01) 96: 69-98 , January 01, 2012

Suppose that a finite population consists of *N* distinct units. Associated with the *i*th 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.

## Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors

### AStA Advances in Statistical Analysis (2016-12-22): 1-25 , December 22, 2016

In this paper, the strong laws of large numbers for partial sums and weighted sums of negatively superadditive-dependent (NSD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type strong law of large numbers. Using these strong laws of large numbers, we further investigate the strong consistency and weak consistency of the LS estimators in the EV regression model with NSD errors, which generalize and improve the corresponding ones for negatively associated random variables. Finally, a simulation is carried out to study the numerical performance of the strong consistency result that we established.