63,996 research outputs found

    Symmetry, regression design, and sampling distributions

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    When values of regressors are symmetrically disposed, many M-estimators in a wide class of models have a reflection property, namely, that as the signs of the coefficients on regressors are reversed, their estimators' sampling distribution is reflected about the origin. When the coefficients are zero, sign reversal can have no effect. So in this case, the sampling distribution of regression coefficient estimators is symmetric about zero, the estimators are median unbiased and, when moments exist, the estimators are exactly uncorrelated with estimators of other parameters. The result is unusual in that it does not require response variates to have symmetric conditional distributions. It demonstrates the potential importance of covariate design in determining the distributions of estimators, and it is useful in designing and interpreting Monte Carlo experiments. The result is illustrated by a Monte Carlo experiment in which maximum likelihood and symmetrically censored least-squares estimators are calculated for small samples from a censored normal linear regression, Tobit, model. © 1994, Cambridge University Press. All rights reserved

    Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator

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    We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges' estimator. The oracle property is often a consequence of sparsity of an estimator. We show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function; in particular, the maximal risk diverges to infinity whenever the loss function is unbounded. For ease of presentation the result is set in the framework of a linear regression model, but generalizes far beyond that setting. In a Monte Carlo study we also assess the extent of the problem in finite samples for the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001). We find that this estimator can perform rather poorly in finite samples and that its worst-case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity.Comment: 18 pages, 5 figure

    Regression Depth and Center Points

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    We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

    Does School Quality Matter? Returns to Education and the Characteristics of Schools in South Africa

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    This paper contributes to what is known about the impact of school quality, by documenting its effect on the incomes of Black South Africans, using data from the 1996 South African census and two national surveys of school quality. South Africa provides an interesting laboratory for studying the impact of school quality on labor market outcomes. Under the Apartheid system, Blacks faced extremely limited residential and school choices, which limits the extent to which results are attributable to the endogeneity of school and residential choice. In addition, Black schools' funding and staffing decisions were made rather arbitrarily by a White government that was at best indifferent to the needs of Black schools. Large differences in pupil/teacher ratios developed between Black schools, differences much larger than those observed in the United States. Using a two-state estimation procedure similar to that employed by Card and Krueger (1992) and by Heckman et al. (1996), we find that the quality of schools in a respondent's magisterial district of origin has a large and significant effect on the rate of return to schooling for Black men. The South African results are notable, moreover, because they are so similar to those estimated by Card and Krueger (1992) for the United States.

    Is there a cross listing premium for non-exchange traded depositary receipts?

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    In this paper, I examine the valuation effects of trading in the U.S. as non-exchange issues i.e. Level 1 and 144 firms for non-U.S. firms. The study is motivated by two facts; first, while the number of new Level 2/3 issues has fallen 2001, Level 1 issues have remained an attractive listing option for non-U.S. firms. Second, while on theoretical grounds, firms from low-disclosure regimes have most to gain from exchange listing; these firms tend to list in the U.S. as non-exchange issues. Here, I examine whether the continuing attractiveness of, and the tendency of firms to choose a Level l/144a listing is value enhancing. My results suggest that the tendency on the part of firms from low-disclosure regimes to choose non-exchange issues is justified. Relative to their high-disclosure peers, these firms tend to gain most from trading in the U.S. However, for Rule 144a issues, the valuation gains are short-lived.Cross listing, Level 1, Rule 144a, Tobin's q

    Allopatric differentiation in the Marcusenius macrolepidotus species complex in southern and eastern Africa: the resurrection of M. pongolensis and M. angolensis, and the description of two new species (Mormyridae, Teleostei)

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    We critically compared local populations of the bulldog fish, Marcusenius macrolepidotus (Peters 1852), from different watersheds, from the furthest south (28° South, South Africa) to the Equator in Kenya. We ascertained allopatric differentiation from topotypical M. macrolepidotus from the Lower Zambezi River (Mozambique) in morphology, electric organ discharges, and molecular genetics for: (1) samples from the Okavango and Upper Zambezi Systems (Botswana and Namibia), (2) samples from South Africa's rivers draining into the Indian Ocean, and (3) samples from the East African Tana River (Kenya). Significant genetic distances in the mitochondrial cytochrome b gene and differing ISSR-PCR profiles corroborate differentiation between the four taxa. We resurrect M. pongolensis (Fowler, 1934) for South Africa (sample 2), and M. angolensis (Boulenger, 1905) for the Quanza River/Angola. We recognize M. altisambesi sp. n. for the Upper Zambezi/Okavango specimens (sample 1), and M. devosi sp. n. for those from Kenya (sample 3)

    Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost

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    We provide a detailed hands-on tutorial for the R add-on package mboost. The package implements boosting for optimizing general risk functions utilizing component-wise (penalized) least squares estimates as base-learners for fitting various kinds of generalized linear and generalized additive models to potentially high-dimensional data. We give a theoretical background and demonstrate how mboost can be used to fit interpretable models of different complexity. As an example we use mboost to predict the body fat based on anthropometric measurements throughout the tutorial

    RURAL-URBAN MIGRATION IN BOLIVIA: AN ESCAPE BOAT?

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    This paper studies rural-urban migration in Bolivia. Domestic migration usually works as an equalization mechanism, in which regions with fewer economic opportunities send migrants to more dynamic regions. We model the migration decision and take into account the possibility of self-selection for computing the returns to migration. We present selectivity corrected quantile regression models for earnings of both migrants and non-migrants in urban and metropolitan areas. We find that migrants receive a premium at low and median quantiles of the urban/metro conditional earnings distribution. This premium is somewhat diminished by a negative selectivity correction for migrants with lower probabilities of migration.
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