COMPSTAT 2004 — Proceedings in Computational Statistics, 2004
ABSTRACT Panel studies in econometrics as well as longitudinal studies in biomedical applications... more ABSTRACT Panel studies in econometrics as well as longitudinal studies in biomedical applications provide data from a sample of individual units where each unit is observed repeatedly over time (age, etc.). In this context, mixed effect models are often applied to analyze the behavior of a response variable in dependence of a number of covariates. In some important applications it is necessary to assume that individual effects vary over time (age, etc.).
The paper is concerned with data from a collection of different, but related, regression curves $... more The paper is concerned with data from a collection of different, but related, regression curves $(m_j0_{j = 1}, \ldots, N, N \gg 1$. In statistical practice, analysis of such data is most frequently based on low-dimensional linear models. It is then assumed that each regression curve $m_j$ is a linear combination of a small number $L \ll N$ of common functions $g_1, \ldots, g_L$k. For example, if all $m_j$'s are straight lines, this holds with $L = 2, g_1 \equiv 1$ and $g_2(x) = x$. In this paper the assumption of a prespecified model is dropped. A nonparametric method is presented which allows estimation of the smallest $L$ and corresponding functions $g_1, \ldots, g_L$ from the data. The procedure combines smoothing techniques with ideas related to principal component analysis. An asymptotic theory is presented with yields detailed insight into properties of the resulting estimators. An application to household expenditure data illustrates the approach.
Non-parametric data envelopment analysis (DEA) estimators based on linear program- ming methods h... more Non-parametric data envelopment analysis (DEA) estimators based on linear program- ming methods have been widely applied in analyses of productive eciency . The distri- butions of these estimators remain unknown except in the simple case of one input and one output. This paper derives the asymptotic distribution of DEA estimators under vari- able returns-to-scale. In addition, two bootstrap procedures (one
We consider functional linear regression where a real variable Y depends on a functional variable... more We consider functional linear regression where a real variable Y depends on a functional variable X. The functional coefficient of the model is estimated by means of smoothing splines. We derive the rates of convergence with respect to the semi-norm induced by the covariance operator of X, which comes to evaluate the error of prediction. These rates, which essentially depend on the smoothness of the function parameter and on the structure of the predictor, are shown to be optimal over a large class of functions parameters and distributions of the predictor.
Given data from a sample of noisy curves in a nonlinear parametric regression model we consider n... more Given data from a sample of noisy curves in a nonlinear parametric regression model we consider nonparametric estimation of the model function and the parameters under certain structural assumptions. An algorithm for a consistent estimator is proposed and examples given.
An index of “behavioral heterogeneity” for every finite population of households is defined. It i... more An index of “behavioral heterogeneity” for every finite population of households is defined. It is shown that the higher the index of behavioral heterogeneity the less sensitive depends the aggregate consumption expenditure ratio upon prices. As a consequence, a high index implies a tendency for the Jacobian of aggregate demand to have a dominant negative diagonal.
This paper introduces a new estimation method for time-varying individual effects in a panel data... more This paper introduces a new estimation method for time-varying individual effects in a panel data model. An important application is the estimation of time-varying tech- nical inefficiencies of individual firms using the fixed effects model. Most models of the stochastic frontier production function require rather strong assumptions about the distribution of technical inefficiency (e.g., half-normal) and random noise (e.g., normal),
A new statistical method is presented for determining an average growth curve which is valid in t... more A new statistical method is presented for determining an average growth curve which is valid in the sense of representing both the average dynamic, or tempo, and the average intensity of the growth process studied. In this context, growth curve means either distance, velocity or acceleration curve. The principal idea is to shift individual curves continuously (and non-linearly) in age to an average developmental age scale. Since the resulting curves represent the typical shape rather than individual variations of it, they are of interest for comparisons of different variables of boys and girls and of subgroups. The method is illustrated with longitudinal growth data from the first Zurich longitudinal study.
The paper deals with different concepts of income elasticities of demand for a heterogenous popul... more The paper deals with different concepts of income elasticities of demand for a heterogenous population and the relationship between individual and aggregate elasticities is analyzed. In general, the aggregate elasticity is not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and magnitude of this term are determined by an empirical analysis based on the U.K. Family Expenditure Survey. It is shown that the relevant quantities can be identified from cross-section data and, without imposing restrictive structural assumptions, can be estimated by nonparametric techniques. It turns out that the aggregate elasticity significantly overestimates the mean of individual elasticities for many commodity groups.
We study changes of the distribution of income, age, occupation, household size via their margina... more We study changes of the distribution of income, age, occupation, household size via their marginal and conditional densities. The data consists of cross sectional samples from the population of Brithish households drawn over the years of 1968 - 1995. Estimation is carried out nonparametrically and no assumptions on the form of the underlying densities is made.
Goodness-of-®t tests based on residual sums of squares are standard procedures used when ®tting r... more Goodness-of-®t tests based on residual sums of squares are standard procedures used when ®tting regression models. Often we have a smooth alternative in mind, a qualitative feature that the ÷ 2 -test does not take into account. We show that the power of detecting a smooth alternative increases when we smooth the current model as well. The proposed test is shown to be able to detect any continuous local alternative tending to zero slower than n 21a2 . Theoretical results also address minimax non-parametric hypothesis testing in Sobolev spaces. A simulation study is presented, and the procedure is applied to expenditure curve estimation.
A method is proposed for modifying the time constant of an EEG amplifier after the recording. It ... more A method is proposed for modifying the time constant of an EEG amplifier after the recording. It is based on digital filtering and works for single sweeps, averaged potentials, and other neurophysiological data, e.g. spontaneous EEG. The validation is based on calibration signals and data from a study on eventrelated potentials.
The paper is about the economic modelling of aggregate consumption expenditure with particular em... more The paper is about the economic modelling of aggregate consumption expenditure with particular emphasis on the distribution effects of income. Under certain assumptions on the evolution over time of the population of households ("structural stability") we shall derive a first order approximation for the change in the aggregate consumption ratio. This approximation allows to analyze whether and how the distribution effect of income affects the aggregate consumption ratio.
Journal of the American Statistical Association, 1995
The shape of a regression curve can to a large extent be characterized by the succession of struc... more The shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema, inflection points, and so on. When analyzing a sample of regression curves, it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample. Such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise. A method is proposed for identifying typical features without relying on an a priori specified functional model for the curves. The approach is based on the frequencies of occurrence of structural features, as, for example, maxima in the curve sample along the x axis. Important tools are nonparametric regression and differentiation and kernel density estimation. Apart from a theoretical foundation, the usefulness of the method is documented by application to two interesting biomedical areas: growth and development, and neurophysiology.
Journal of the American Statistical Association, 1991
... Alois Kneip is doing statistical research in the Sonderforschungsbereich 123 at the In-... Ch... more ... Alois Kneip is doing statistical research in the Sonderforschungsbereich 123 at the In-... Chiu (1990) has pro-posed a different approach to deal with variability of band-width selectors in nonparametric regression, based on a time series approach with equally spaced data. ...
COMPSTAT 2004 — Proceedings in Computational Statistics, 2004
ABSTRACT Panel studies in econometrics as well as longitudinal studies in biomedical applications... more ABSTRACT Panel studies in econometrics as well as longitudinal studies in biomedical applications provide data from a sample of individual units where each unit is observed repeatedly over time (age, etc.). In this context, mixed effect models are often applied to analyze the behavior of a response variable in dependence of a number of covariates. In some important applications it is necessary to assume that individual effects vary over time (age, etc.).
The paper is concerned with data from a collection of different, but related, regression curves $... more The paper is concerned with data from a collection of different, but related, regression curves $(m_j0_{j = 1}, \ldots, N, N \gg 1$. In statistical practice, analysis of such data is most frequently based on low-dimensional linear models. It is then assumed that each regression curve $m_j$ is a linear combination of a small number $L \ll N$ of common functions $g_1, \ldots, g_L$k. For example, if all $m_j$'s are straight lines, this holds with $L = 2, g_1 \equiv 1$ and $g_2(x) = x$. In this paper the assumption of a prespecified model is dropped. A nonparametric method is presented which allows estimation of the smallest $L$ and corresponding functions $g_1, \ldots, g_L$ from the data. The procedure combines smoothing techniques with ideas related to principal component analysis. An asymptotic theory is presented with yields detailed insight into properties of the resulting estimators. An application to household expenditure data illustrates the approach.
Non-parametric data envelopment analysis (DEA) estimators based on linear program- ming methods h... more Non-parametric data envelopment analysis (DEA) estimators based on linear program- ming methods have been widely applied in analyses of productive eciency . The distri- butions of these estimators remain unknown except in the simple case of one input and one output. This paper derives the asymptotic distribution of DEA estimators under vari- able returns-to-scale. In addition, two bootstrap procedures (one
We consider functional linear regression where a real variable Y depends on a functional variable... more We consider functional linear regression where a real variable Y depends on a functional variable X. The functional coefficient of the model is estimated by means of smoothing splines. We derive the rates of convergence with respect to the semi-norm induced by the covariance operator of X, which comes to evaluate the error of prediction. These rates, which essentially depend on the smoothness of the function parameter and on the structure of the predictor, are shown to be optimal over a large class of functions parameters and distributions of the predictor.
Given data from a sample of noisy curves in a nonlinear parametric regression model we consider n... more Given data from a sample of noisy curves in a nonlinear parametric regression model we consider nonparametric estimation of the model function and the parameters under certain structural assumptions. An algorithm for a consistent estimator is proposed and examples given.
An index of “behavioral heterogeneity” for every finite population of households is defined. It i... more An index of “behavioral heterogeneity” for every finite population of households is defined. It is shown that the higher the index of behavioral heterogeneity the less sensitive depends the aggregate consumption expenditure ratio upon prices. As a consequence, a high index implies a tendency for the Jacobian of aggregate demand to have a dominant negative diagonal.
This paper introduces a new estimation method for time-varying individual effects in a panel data... more This paper introduces a new estimation method for time-varying individual effects in a panel data model. An important application is the estimation of time-varying tech- nical inefficiencies of individual firms using the fixed effects model. Most models of the stochastic frontier production function require rather strong assumptions about the distribution of technical inefficiency (e.g., half-normal) and random noise (e.g., normal),
A new statistical method is presented for determining an average growth curve which is valid in t... more A new statistical method is presented for determining an average growth curve which is valid in the sense of representing both the average dynamic, or tempo, and the average intensity of the growth process studied. In this context, growth curve means either distance, velocity or acceleration curve. The principal idea is to shift individual curves continuously (and non-linearly) in age to an average developmental age scale. Since the resulting curves represent the typical shape rather than individual variations of it, they are of interest for comparisons of different variables of boys and girls and of subgroups. The method is illustrated with longitudinal growth data from the first Zurich longitudinal study.
The paper deals with different concepts of income elasticities of demand for a heterogenous popul... more The paper deals with different concepts of income elasticities of demand for a heterogenous population and the relationship between individual and aggregate elasticities is analyzed. In general, the aggregate elasticity is not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and magnitude of this term are determined by an empirical analysis based on the U.K. Family Expenditure Survey. It is shown that the relevant quantities can be identified from cross-section data and, without imposing restrictive structural assumptions, can be estimated by nonparametric techniques. It turns out that the aggregate elasticity significantly overestimates the mean of individual elasticities for many commodity groups.
We study changes of the distribution of income, age, occupation, household size via their margina... more We study changes of the distribution of income, age, occupation, household size via their marginal and conditional densities. The data consists of cross sectional samples from the population of Brithish households drawn over the years of 1968 - 1995. Estimation is carried out nonparametrically and no assumptions on the form of the underlying densities is made.
Goodness-of-®t tests based on residual sums of squares are standard procedures used when ®tting r... more Goodness-of-®t tests based on residual sums of squares are standard procedures used when ®tting regression models. Often we have a smooth alternative in mind, a qualitative feature that the ÷ 2 -test does not take into account. We show that the power of detecting a smooth alternative increases when we smooth the current model as well. The proposed test is shown to be able to detect any continuous local alternative tending to zero slower than n 21a2 . Theoretical results also address minimax non-parametric hypothesis testing in Sobolev spaces. A simulation study is presented, and the procedure is applied to expenditure curve estimation.
A method is proposed for modifying the time constant of an EEG amplifier after the recording. It ... more A method is proposed for modifying the time constant of an EEG amplifier after the recording. It is based on digital filtering and works for single sweeps, averaged potentials, and other neurophysiological data, e.g. spontaneous EEG. The validation is based on calibration signals and data from a study on eventrelated potentials.
The paper is about the economic modelling of aggregate consumption expenditure with particular em... more The paper is about the economic modelling of aggregate consumption expenditure with particular emphasis on the distribution effects of income. Under certain assumptions on the evolution over time of the population of households ("structural stability") we shall derive a first order approximation for the change in the aggregate consumption ratio. This approximation allows to analyze whether and how the distribution effect of income affects the aggregate consumption ratio.
Journal of the American Statistical Association, 1995
The shape of a regression curve can to a large extent be characterized by the succession of struc... more The shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema, inflection points, and so on. When analyzing a sample of regression curves, it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample. Such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise. A method is proposed for identifying typical features without relying on an a priori specified functional model for the curves. The approach is based on the frequencies of occurrence of structural features, as, for example, maxima in the curve sample along the x axis. Important tools are nonparametric regression and differentiation and kernel density estimation. Apart from a theoretical foundation, the usefulness of the method is documented by application to two interesting biomedical areas: growth and development, and neurophysiology.
Journal of the American Statistical Association, 1991
... Alois Kneip is doing statistical research in the Sonderforschungsbereich 123 at the In-... Ch... more ... Alois Kneip is doing statistical research in the Sonderforschungsbereich 123 at the In-... Chiu (1990) has pro-posed a different approach to deal with variability of band-width selectors in nonparametric regression, based on a time series approach with equally spaced data. ...
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