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Title:

Demand Analysis as an Ill-Posed Inverse Problem with Semiparametric Specification

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In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly ...

In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive results characterizing the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze the finite sample behavior of the proposed estimator. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages, and the difficulties of an approach which leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between nonparametric instrumental variable models, and the recently emphasized issue of unobserved heterogeneity in structural models. ; Instrumental variables; Inverse problem; Nonparametric regression, Consumer Demand, Convergence rates Minimize

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preprint

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Title:

Likelihood Ratio Testing for Hidden Markov Models Under Non-standard Conditions

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In practical applications, when testing parametric restrictions for hidden Markov models (HMMs), one frequently encounters non-standard situations such as testing for zero entries in the transition matrix, one-sided tests for the parameters of the transition matrix or for the components of the stationary distribution of the underlying Markov cha...

In practical applications, when testing parametric restrictions for hidden Markov models (HMMs), one frequently encounters non-standard situations such as testing for zero entries in the transition matrix, one-sided tests for the parameters of the transition matrix or for the components of the stationary distribution of the underlying Markov chain, or testing boundary restrictions on the parameters of the state-dependent distributions. In this paper, we briefly discuss how the relevant asymptotic distribution theory for the likelihood ratio test (LRT) when the true parameter is on the boundary extends from the independent and identically distributed situation to HMMs. Then we concentrate on discussing a number of relevant examples. The finite-sample performance of the LRT in such situations is investigated in a simulation study. An application to series of epileptic seizure counts concludes the paper. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008. Minimize

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article

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Title:

Integrated Square Error Asymptotics for Supersmooth Deconvolution

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We derive the asymptotic distribution of the integrated square error of a deconvolution kernel density estimator in supersmooth deconvolution problems. Surprisingly, in contrast to direct density estimation as well as ordinary smooth deconvolution density estimation, the asymptotic distribution is no longer a normal distribution but is given by ...

We derive the asymptotic distribution of the integrated square error of a deconvolution kernel density estimator in supersmooth deconvolution problems. Surprisingly, in contrast to direct density estimation as well as ordinary smooth deconvolution density estimation, the asymptotic distribution is no longer a normal distribution but is given by a normalized chi-squared distribution with 2 d.f. A simulation study shows that the speed of convergence to the asymptotic law is reasonably fast. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics. Minimize

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Title:

A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU

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Bimodality, Convergence analysis, Cross-sectional income distribution, Likelihood ratio test, Finite mixture

Bimodality, Convergence analysis, Cross-sectional income distribution, Likelihood ratio test, Finite mixture Minimize

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Title:

Perspectives on the World Income Distribution - Beyond Twin Peaks Towards Welfare Conclusions

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This paper contributes towards the growing debate concerning the world distribution of income and its evolution over that past three to four decades. Our methodological approach is twofold. First, we formally test for the number of modes in a cross-sectional analysis where each country is represented by one observation. We contribute to existing...

This paper contributes towards the growing debate concerning the world distribution of income and its evolution over that past three to four decades. Our methodological approach is twofold. First, we formally test for the number of modes in a cross-sectional analysis where each country is represented by one observation. We contribute to existing studies with technical improvements of the testing procedure, enabling us to draw new conclusions, and an extension of the time horizon being analyzed. Second, we estimate a global distribution of income from national log-normal distributions of income, as well as a global distribution of log-income as a mixture of national normal distributions of log-income. From this distribution we obtain measures for global inequality and poverty as well as global growth incidence curves. ; Convergence, Silverman\'s test, non-parametric statistics, bimodal, global income distribution, poverty, inequality, growth incidence curves Minimize

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Title:

Identifiability of Finite Mixtures of Elliptical Distributions

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We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate "t"-distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the ...

We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate "t"-distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the mixture, in addition to the location vector and the scatter matrix. Furthermore, we discuss the identifiability of finite mixtures of elliptical densities with generators that correspond to scale mixtures of normal distributions. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics. Minimize

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Title:

Twin Peaks or Three Components? - Analyzing the World\'s Cross-Country Distribution of Income

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In this paper we analyze the world´s cross-national distribution of income and its evolution from 1970 to 2003. We argue that modeling this distribution by a finite mixture and investigating its number of components has advantages over nonparametric inference concerning the number of modes. In particular, the number of components of the distribu...

In this paper we analyze the world´s cross-national distribution of income and its evolution from 1970 to 2003. We argue that modeling this distribution by a finite mixture and investigating its number of components has advantages over nonparametric inference concerning the number of modes. In particular, the number of components of the distribution does not depend on the scale chosen (original or logarithmic), whereas the number of modes does. Instead of so-called twin-peaks, we find that the distribution appears to have only two components in 1970-1975, but consists of three components from 1976 onwards, a low, average and high mean-income group, with group means diverging over time. Here we apply recently developed modified likelihood ratio tests for the number of components in a finite mixture. The intra distributional dynamics are investigated in detail using posterior probability estimates. ; cross-national income distribution; mixture models; modified likelihood ratio test; nonparametric density estimation Minimize

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Title:

Income Distribution Dynamics and Pro-Poor Growth in the World from 1970 to 2003

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We estimate and analyze the global income distribution from national log-normal income distributions for the years 1970 to 2003, as well as the income distribution of seven regional subsamples. From these distributions we obtain measures for global and regional inequality and poverty, and find decreasing global poverty and inequality during the ...

We estimate and analyze the global income distribution from national log-normal income distributions for the years 1970 to 2003, as well as the income distribution of seven regional subsamples. From these distributions we obtain measures for global and regional inequality and poverty, and find decreasing global poverty and inequality during the time period. By decomposing inequality into within and between country inequality using Theils’ measure of inequality, we observe declining inequality between countries whereas overall inequality within countries increased. Furthermore, we calculate growth incidence curves for five year periods between 1970 and 2003, as well as a growth incidence curve for the entire period and corresponding rates of pro-poor growth. In the global income distribution, the 8.5th to 63.5th global income percentiles experienced above average percentile growth rates, while the remaining very lowest quantiles experienced also the lowest percentile growth rates. Using the regional decomposition we find that while in 1970 more than half of the worlds extreme poor and poor people lived in East Asia, it is Sub-Saharan Africa where nowadays two thirds of the extreme poor and half of the worlds poor live. ; Global income distribution, poverty, inequality, growth incidence curves, pro-poor growth convergence Minimize

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Title:

Demand Analysis as an Ill-Posed Inverse Problem with Semiparametric Specification

Description:

In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly ...

In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive results characterizing the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze the finite sample behavior of the proposed estimator. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages, and the difficulties of an approach which leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between nonparametric instrumental variable models, and the recently emphasized issue of unobserved heterogeneity in structural models. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-11-24

Source:

http://fmwww.bc.edu/ec-p/wp752.pdf

http://fmwww.bc.edu/ec-p/wp752.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Instrumental variables ; Inverse problem ; Nonparametric regression ; Consumer Demand ; Convergence rates

Instrumental variables ; Inverse problem ; Nonparametric regression ; Consumer Demand ; Convergence rates Minimize

DDC:

330 Economics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Testing for Image Symmetries – with Application to Confocal Microscopy

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Statistical tests are introduced for checking whether an image function f(x,y) defined on the unit disc D = {(x,y) : x 2 + y 2 ≤ 1} is invariant under certain symmetry transformations of D, given that discrete and noisy data are observed. We consider invariance under reflections or under rotations by rational angles, as well as joint invariance ...

Statistical tests are introduced for checking whether an image function f(x,y) defined on the unit disc D = {(x,y) : x 2 + y 2 ≤ 1} is invariant under certain symmetry transformations of D, given that discrete and noisy data are observed. We consider invariance under reflections or under rotations by rational angles, as well as joint invariance under both reflections and rotations. Furthermore, we propose a test for rotational invariance of f(x,y), i.e., for checking whether f(x,y), after transformation to polar coordinates, only depends on the radius and not on the angle. These symmetry relations can be naturally expressed as restrictions for the Zernike moments of the image function f(x,y), i.e., the Fourier coefficients with respect to the Zernike orthogonal basis. Therefore, our test statistics are based on checking whether the estimated Zernike coefficients approximately satisfy those restrictions. This is carried out by forming the L2 distance between the image function and its transformed version obtained by some symmetry transformation. We derive the asymptotic distribution of the test statistics under both the hypothesis of symmetry as well as under fixed alternatives. Furthermore, we investigate the quality of the asymptotic approximations via simulation studies. The usefulness our theory is verified by examining an important problem in confocal microscopy, i.e., we investigate possible imprecise alignments in the optical path of the microscope. For optical systems with rotational symmetry, the theoretical point-spread-function (PSF) is reflection symmetric with respect to two orthogonal axes, and rotationally invariant if the detector plane matches the optical plane of the microscope. We use our tests to investigate whether the required symmetries can indeed be detected in the empirical PSF. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-21

Source:

http://www.ruhr-uni-bochum.de/imperia/md/content/mathematik3/publications/testing_for_image_symmetries___revision.pdf

http://www.ruhr-uni-bochum.de/imperia/md/content/mathematik3/publications/testing_for_image_symmetries___revision.pdf Minimize

Document Type:

text

Language:

en

Subjects:

3

3 Minimize

DDC:

515 Analysis *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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