Abstract
Smith (1994) proposes estimation in linear regression models with non-negative errors by maximizing the sum of fitted values subject to the constraint that the fitted values can be no larger than the corresponding response value. In this paper, we consider the limiting distribution of these estimators under very general conditions. Some extensions to local polynomial estimation are also considered.
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References
An, H.Z. and Huang, F.C., “Estimation for regressive and autoregressive model with nonnegative residual errors,” Journal of Time Series Analysis 14, 179-191, (1993).
Andel, J., “Nonnegative autoregressive processes,” Journal of Time Series Analysis 10, 1–11, (1989).
Chernozhukov, V., “Nonparametric extreme regression quantiles,” Unpublished manuscript, 1998.
Chernozhukov, V., “Conditional extremes and near extremes: estimation, inference and economic applications,” Ph.D. thesis, Department of Economics, Stanford University, 2000.
Feigin, P.D. and Resnick, S.I., “Limit distributions for linear programming time series estimators,” Stochastic Processes and their Applications 51, 135–166, (1994).
Geyer, C.J., “On the asymptotics of constrained M-estimation,” Annals of Statistics 22, 1993–2010, (1994).
Geyer, C.J., “On the asymptotics of convex stochastic optimization,” Unpublished manuscript, 1996.
Kallenberg, O., Random Measures, (third edition), Akademie-Verlag, 1983.
Knight, K., “Epi-convergence in distribution and stochastic equi-emicontinuity,” Unpublished manuscript, 1999.
Koenker, R. and Bassett, G., “Regression quantiles,” Econometrica 46, 33–50, (1978).
Leadbetter, M.R., Lindgren, G., and Rootzén, H., Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.
Nielsen, B. and Shephard, N., “Likelihood analysis of a first order autoregressive model with exponential innovations,” Unpublished manuscript, 1999.
Pflug, G.Ch., “On an argmax-distribution connected to the Poisson process,” In: Asymptotic Statistics (P. Mandl and M. Hušková, eds) Physica-Verlag, Heidelberg, 123–130, (1994).
Pflug, G. Ch., “Asymptotic stochastic programs,” Mathematics of Operations Research 20, 769–789, (1995).
Portnoy, S. and Jurečková, J., “On extreme regression quantiles,” Extremes 2, 227–243, (1999).
Smith, R.L., “Nonregular regression,” Biometrika 81, 173–183, (1994).
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Knight, K. Limiting Distributions of Linear Programming Estimators. Extremes 4, 87–103 (2001). https://doi.org/10.1023/A:1013991808181
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DOI: https://doi.org/10.1023/A:1013991808181