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48
Least angle regression
 Ann. Statist
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 759 (35 self)
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The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS modification efficiently implements Forward Stagewise linear regression, another promising
Spatial Econometrics
 PALGRAVE HANDBOOK OF ECONOMETRICS: VOLUME 1, ECONOMETRIC THEORY
, 2001
"... Spatial econometric methods deal with the incorporation of spatial interaction and spatial structure into regression analysis. The field has seen a recent and rapid growth spurred both by theoretical concerns as well as by the need to be able to apply econometric models to emerging large geocoded da ..."
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Cited by 64 (5 self)
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Spatial econometric methods deal with the incorporation of spatial interaction and spatial structure into regression analysis. The field has seen a recent and rapid growth spurred both by theoretical concerns as well as by the need to be able to apply econometric models to emerging large geocoded data bases. The review presented in this chapter outlines the basic terminology and discusses in some detail the specification of spatial effects, estimation of spatial regression models, and specification tests for spatial effects.
The Decomposition of Promotional Response: An Empirical Generalization
 Marketing Science
, 1999
"... Price promotions are used extensively in marketing for one simple reason  consumers respond. The sales increase for a brand on promotion could be due to consumers accelerating their purchases (i.e., buying earlier than usual and/or buying more than usual) and/or consumers switching their choice ..."
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Cited by 37 (4 self)
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Price promotions are used extensively in marketing for one simple reason  consumers respond. The sales increase for a brand on promotion could be due to consumers accelerating their purchases (i.e., buying earlier than usual and/or buying more than usual) and/or consumers switching their choice from other brands. Purchase acceleration and brand switching relate to the primary demand and secondary demand effects of a promotion. Gupta (1988) captures these effects in a single model and decomposes a brand's total price elasticity into these components. He reports, for the coffee product category, that the main impact of a price promotion is on brand choice (84%), and that there is a smaller impact on purchase incidence (14%) and stockpiling (2%). In other words, the majority of the effect of a promotion is at the secondary level (84%) and there is a relatively small primary demand effect (16%). This paper reports the decomposition of total price elasticity for 173 brands acros...
The Proximity of an Individual to a Population With Applications in Discriminant Analysis
, 1995
"... : We develop a proximity function between an individual and a population from a distance between multivariate observations. We study some properties of this construction and apply it to a distancebased discrimination rule, which contains the classic linear discriminant function as a particular ..."
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Cited by 18 (10 self)
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: We develop a proximity function between an individual and a population from a distance between multivariate observations. We study some properties of this construction and apply it to a distancebased discrimination rule, which contains the classic linear discriminant function as a particular case. Additionally, this rule can be used advantageously for categorical or mixed variables, or in problems where a probabilistic model is not well determined. This approach is illustrated and compared with other classic procedures using four real data sets. Keywords: Categorical and mixed data; Distances between observations; Multidimensional scaling; Discrimination; Classification rules. AMS Subject Classification: 62H30 The authors thank M.Abrahamowicz, J. C. Gower and M. Greenacre for their helpful comments, and W. J. Krzanowski for providing us with a data set and his quadratic location model program. Work supported in part by CGYCIT grant PB930784. Authors' address: Departam...
From association to causation via regression
 Indiana: University of Notre Dame
, 1997
"... For nearly a century, investigators in the social sciences have used regression models to deduce causeandeffect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend ..."
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Cited by 16 (6 self)
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For nearly a century, investigators in the social sciences have used regression models to deduce causeandeffect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work a principle honored more often in the breach than the observance.
A Unified Measure of Uncertainty of Estimated Best Linear Unbiased Predictor in SmallArea Estimation Problems
, 1997
"... this paper addresses an important open problem raised by Cox and Reid (1987) in smallarea prediction using conditional profile likelihood method. ..."
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Cited by 15 (4 self)
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this paper addresses an important open problem raised by Cox and Reid (1987) in smallarea prediction using conditional profile likelihood method.
On Selection Biases in BooktoMarket Based Tests of Asset Pricing Models
, 1995
"... Many studies have documented portfolio strategies that provide returns in excess of those expected, given the level of risk of the portfolio. Variables that seem to have predictive power for equity returns include the market capitalization of the firm’s equity and the ratio of the firm’s book equity ..."
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Cited by 15 (0 self)
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Many studies have documented portfolio strategies that provide returns in excess of those expected, given the level of risk of the portfolio. Variables that seem to have predictive power for equity returns include the market capitalization of the firm’s equity and the ratio of the firm’s book equity to market equity (BE/ME). Firms with low market capitalization and high booktomarket values seem to earn high returns. With respect to the booktomarket anomaly, it has been argued that the apparent superior performance is due to a subtle selection bias in a typical data source used to implement the tests of asset pricing models, the COMPUSTAT data. We use a sample of COMPUSTAT data that is free from this bias to investigate whether the previous evidence on the booktomarket anomaly is an artifact of this selection bias. The postulated selection bias does not seem to be important for samples restricted to NYSE/AMEX firms. There is some difference when NASDAQ firms are included in the standard COMPUSTAT sample. This may be due to a truly stronger BE/ME effect or to a more severe selection bias in that sample. Our data do not allow us to disentangle these two possible explanations.
Design and analysis of MIMO spatial multiplexing systems with quantized feedback
 IEEE Trans. Signal Processing
, 2006
"... Abstract—This paper investigates the problem of transmit beamforming in multipleantenna spatial multiplexing (SM) systems employing a finiterate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new criterion for designing the codebook of beamfo ..."
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Cited by 14 (2 self)
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Abstract—This paper investigates the problem of transmit beamforming in multipleantenna spatial multiplexing (SM) systems employing a finiterate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new criterion for designing the codebook of beamforming matrices that is based on minimizing an approximation to the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to a locally optimum codebook. Under the independent identically distributed channel and high signaltonoise ratio (SNR) assumption, the effect on channel capacity of the finitebit representation of the beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multimode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits resulting in a practical and efficient multipleinput multipleoutput system design. Index Terms—Channel capacity, channel information feedback, matrix quantization, multiple antennas, multipleinput multipleoutput (MIMO) systems, spatial multiplexing, transmit beamforming. I.
Refining 3D Reconstructions: A Theoretical and Experimental Study of the Effect of CrossCorrelations
 CVGIP:IU
, 1994
"... In robot navigation a model of the environment needs to be reconstructed for various applications, including path planning, obstacle avoidance and determining where the robot is located. Traditionally, the model was acquired using two images (twoframe Structure from Motion) but the acquired models ..."
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Cited by 13 (5 self)
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In robot navigation a model of the environment needs to be reconstructed for various applications, including path planning, obstacle avoidance and determining where the robot is located. Traditionally, the model was acquired using two images (twoframe Structure from Motion) but the acquired models were unreliable and inaccurate. Recently, research has shifted to using several frames (multiframe Structure from Motion) instead of just two frames. However, almost none of the reported multiframe algorithms has produced accurate and stable reconstructions for general robot motion. The main reason seems to be that the primary source of error in the reconstruction  the error in the underlying motion  has been mostly ignored. Intuitively, if a reconstruction of the scene is made up of points, this motion error affects each reconstructed point in a systematic way. For example, if the translation of the robot is erroneous in a certain direction, all the reconstructed points would be sh...
The local bootstrap for Markov processes
 J. Statist. Plann. Inference
, 2002
"... A nonparametric bootstrap procedure is proposed for stochastic processes which follow a general autoregressive structure. The procedure generates bootstrap replicates by locally resampling the original set of observations reproducing automatically its dependence properties. It avoids an initial non ..."
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Cited by 13 (2 self)
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A nonparametric bootstrap procedure is proposed for stochastic processes which follow a general autoregressive structure. The procedure generates bootstrap replicates by locally resampling the original set of observations reproducing automatically its dependence properties. It avoids an initial nonparametric estimation of process characteristics in order to generate the pseudotime series and the bootstrap replicates mimic several of the properties of the original process. Applications of the procedure in nonlinear time series analysis are considered and theoretically justi ed; some simulated and real data examples are discussed.