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A Brief Overview of Nonparametric Methods in Economics

Published online by Cambridge University Press:  10 May 2017

Arne Hallam*
Affiliation:
Department of Economics, Iowa State University
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The concept of nonparametric analysis, estimation, and inference has a long and storied existence in the annals of economic measurement. At least four rather distinct types of analysis are lumped under the broad heading of nonparametrics. The oldest, and perhaps most common, is that associated with distribution-free methods and order statistics. Similar in spirit, but different in emphasis, is nonparametric density estimation, such as the currently popular kernel estimator for regression. Semi-parametric or semi-nonparametric estimation combines parametric analysis of portions of the problem with nonparametric specification for the remainder, such as the specification of a specific functional form for a regression function with a nonparametric representation of the error distribution. The final type of nonparametrics is that associated with data envelopment analysis and revealed preference, although the use of the term nonparametrics for this research is perhaps a misnomer. This paper will briefly review each of the four types of analysis, leaning heavily on other published work for more detailed exposition. The paper will then discuss in more detail the application of the revealed-preference approach to four specific economic problems: efficiency, the structure of technology or preferences, technical or taste change, and risky choice. The paper is not complete, exhaustive, or detailed. The primary purpose is to expose the reader to a variety of techniques and provide ample reference to the relevant literature.

Type
Invited Presentation
Copyright
Copyright © 1992 Northeastern Agricultural and Resource Economics Association 

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Footnotes

Journal Paper no. J-15075 of the Iowa Agricultural and Home Economics Experiment Station, Ames, IA. Project no. 2894.

References

Afriat, S.N.The Construction of Utility Functions from Expenditure Data.” International Economic Review 8 (1967):6777.Google Scholar
Afriat, S.N.Efficiency Estimation of Production Functions.” International Economic Review 13 (1972):568–98.Google Scholar
Afriat, S.N.On A System of Inequalities in Demand Analysis: An Extension of the Classical Method.” International Economic Review 14 (1973):460–72.Google Scholar
Aigner, D., and Chu, S.F.On Estimating the Industry Production Function.” American Economic Review 58 (1968):826–39.Google Scholar
Aigner, D., Lovell, C.A. Knox, and Schmidt, P.Formulation and Estimation of Stochastic Frontier Production Function Models.” Journal of Econometrics 6 (1977):2137.Google Scholar
Aizcorbe, A.M.A Lower Bound for the Power of Nonparametric Tests.” Journal of Business and Economic Statistics 9 (1991):463–67.Google Scholar
Alston, J.M., and Chalfant, J.A.Can We Take the Con Out of Meat Demand Studies.” Western Journal of Agricultural Economics 16 (1991):3648.Google Scholar
Andrews, D.W.K.Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models.” Econometrica 59 (1991):307–46.Google Scholar
Banker, R.D., Chames, A., and Cooper, W.W.Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis.” Management Science 30 (1984):1078–92.Google Scholar
Banker, R.D., Chames, A., Cooper, W.W., and Maindiratta, A.A Comparison of DEA and Translog Estimates of Production Frontiers Using Simulated Observations from a Known Technology.” In Applications of Modern Production Theory: Efficiency and Productivity, edited by Dogramaci, A. and Fare, R. Boston: Kluwer Academic Publishers, 1988.Google Scholar
Banker, R.D., and Maindiratta, A.Nonparametric Analysis of Technical and Allocative Efficiencies in Production.” Econometrica 56 (1988):1315–32.Google Scholar
Banker, R.D., Conrad, R., and Strauss, R.P.A Comparative Application of Data Envelopment Analysis and Translog Methods: An Illustrative Study of Hospital Production.” Management Science 32 (1986):3043.Google Scholar
Barnett, W.A., and Yue, P.Semiparametric Estimation of the Asymptotically Ideal Model: The AIM Demand System.” In Advances in Econometrics, vol. 7, edited by Rhodes, G.F. and Fomby, T.B. Greenwich: JAI Press, 1988.Google Scholar
Barnett, W.A., and Lee, Y.W.The Global Properties of the Minflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms.” Econometrica 53 (1985):1421–37.Google Scholar
Barnhart, S.W., and Whitney, G.A.Nonparametric Analysis in Parametric Estimation: An Application to Translog Demand Systems.” Review of Economics and Statistics 70 (1988):149–53.Google Scholar
Battese, G.E., and Coelli, T.J.Prediction of Firm-level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data.” Journal of Econometrics 38 (1988):387–99.Google Scholar
Bauer, P.W.Recent Developments in the Econometric Estimation of Frontiers.” Journal of Econometrics 46 (1990):3956.Google Scholar
Bierens, H.Kernel Estimation of Regression Functions.” In Advances in Econometrics, Fifth World Congress, vol. 1, edited by Bewley, T. Cambridge: Cambridge University Press, 1987.Google Scholar
Blackorby, C., Primont, D., and Russell, R.R. Duality, Separability, and Functional Structure: Theory and Applications. New York: North Holland, 1978.Google Scholar
Boles, J.Efficiency Squared-Efficient Computation of Efficiency Indexes.” In Proceedings Thirty-ninth Annual Meeting, Western Farm Economics Association. 1966.Google Scholar
Boles, J. The 1130 Farrell Efficiency System—Multiple Products, Multiple Factors. Berkeley: Giannini Foundation of Agricultural Economics, 1971.Google Scholar
Bressler, R.G.The Measurement of Productive Efficiency.” In Proceedings Thirty-ninth Annual Meeting, Western Farm Economics Association. 1966.Google Scholar
Bronars, S.G.The Power of Nonparametric Tests of Preference Maximization.” Econometrica 55 (1987):693–98.Google Scholar
Browning, M.A Nonparametric Test of the Life-Cycle Rational Expectations Hypothesis.” International Economic Review 30 (1989):979–92.Google Scholar
Byrnes, P., Färe, R., and Grosskopf, S.Measuring Productive Efficiency: An Application to Illinois Strip Mines.” Management Science 30 (1984):671–81.Google Scholar
Byrnes, P., Färe, R., Grosskopf, S., and Kraft, S.Technical Efficiency and Size: The Case of Illinois Grain Farms.” European Review of Agricultural Economics 14, no. 4 (1987):367–82.Google Scholar
Campbell, B., and Dufour, J.Over-rejections in Rational Expectations Models.” Economics Letters 35 (1991):285–90.Google Scholar
Chalfant, J.A.A Globally Flexible, Almost Ideal Demand System.” Journal of Business and Economic Statistics 5 (1987):233–42.Google Scholar
Chalfant, J.A., and Alston, J.M.Accounting for Changes in Tastes.” Journal of Political Economy 96 (1988):391410.Google Scholar
Chamberlain, G.Asymptotic Efficiency in Estimation with Conditional Moment Restrictions.” Journal of Econometrics 34 (1987):305–34.Google Scholar
Chamberlain, G.Efficiency Bounds for Semiparametric Regression.” Econometrica 60 (1992):567–96.Google Scholar
Charnes, A., Cooper, W.W., Golany, B., Seiford, L., and Stutz, J.Foundations of Data Envelopment Analysis for Pareto-Koppmans Efficient Empirical Production Functions.” Journal of Econometrics 30 (1985):91107.Google Scholar
Chavas, J., and Cox, T.L.A Nonparametric Analysis of Agricultural Technology.” American Journal of Agricultural Economics 70 (1988):303–10.Google Scholar
Chavas, J., and Cox, T.L.A Nonparametric Analysis of Productivity: The Case of U.S. and Japanese Manufacturing.” American Economic Review 80 (1990):450–64.Google Scholar
Coslett, S.R.Efficiency Bounds For Distribution Free Estimators of the Binary Choice Model and the Censored Regression Models.” Econometrica 55 (1987):559–85.Google Scholar
Deaton, A.S.Rice Prices and Income Distribution in Thailand.” Economic Journal 99 (1989):137.Google Scholar
Diewert, W.E.Afriat and Revealed Preference Theory.” Review of Economic Studies 40(1973a):419–26.Google Scholar
Diewert, W.E.Functional Forms for Profit and Transformation Functions.” Journal of Economic Theory 6(1973b):284316.Google Scholar
Diewert, W.E.Hick's Aggregation Theorem and the Existence of a Real Value Added Function.” In Production Economics: A Dual Approach to Theory and Practice, edited by Fuss, M. and McFadden, D. Amsterdam: North Holland, 1978.Google Scholar
Diewert, W.E., and Parkin, C.Linear Programming Tests of Regularity Conditions for Production Functions.” In Quantitative Studies on Production and Prices, edited by Eichorn, W., Henn, R., Newmann, K., and Shephard, R.W. Wurzburg-Wien: Physica-Verlag, 1983.Google Scholar
Diewert, W.E., and Parkin, C.Tests for the Consistency of Consumer Data.” Journal of Econometrics 30 (1985):127–47.Google Scholar
Diewert, W.E., and Wales, T.J.Flexible Functional Forms and Global Curvature Conditions.” Econometrica 55 (1987):4368.Google Scholar
Engle, R.F., Granger, C.W.J., Rice, J., and Weiss, A.Semiparametric Estimates of the Relation Between Weather and Electricity Sales.” Journal of the American Statistical Association 81(1986);310–20.Google Scholar
Epanechinikov, V.A.Nonparametric Estimation of a Multivariate Probability Density.” Theory of Probability and Its Applications 14 (1969):153–58.Google Scholar
Epstein, L.G., and Yatchew, A.J.Nonparametric Hypothesis Testing Procedures and Applications to Demand Analysis.” Journal of Econometrics 30 (1985):149–69.Google Scholar
Färe, R. Fundamentals of Production Theory. New York: Springer-Verlag, 1988.Google Scholar
Färe, R., Grabowski, R., and Grosskopf, S.Technical Efficiency of Philippine Agriculture.” Applied Economics 17 (1985):205–14.Google Scholar
Färe, R., Grosskopf, S., and Lovell, C.A. Knox The Measurement of Efficiency of Production. Boston: Kluwer-Nijhoff, 1985.Google Scholar
Färe, R., Grosskopf, S., and Kokkelenberg, E.C.Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach.” International Economic Review 30 (1989):655–66.Google Scholar
Farrell, M.J.The Measurement of Economic Efficiency.” Journal of the Royal Statistical Society 120, Pt. III(1957):252–81.Google Scholar
Fawson, C., and Shumway, C.R.A Nonparametric Investigation of Agricultural Production Behavior for U.S. Subregions.” American Journal of Agricultural Economics 70 (1988):311–17.Google Scholar
Friedman, M.The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance.” Journal of the American Statistical Association 32 (1937):675701.Google Scholar
Gallant, A.R.On the Bias in Flexible Functional Forms and an Essentially Unbiased Form: The Fourier Flexible Form.” Journal of Econometrics 15 (1981):211–45.Google Scholar
Gallant, A.R.Unbiased Determination of Production Technologies.” Journal of Econometrics 20 (1982):285323.Google Scholar
Gallant, A.R.The Fourier Flexible Form.” American Journal of Agricultural Economics 66 (1984):204–8.Google Scholar
Gallant, A.R., and Nychka, D.W.Semi-nonparametric Maximum Likelihood Estimation.” Econometrica 55 (1987):363–90.Google Scholar
Gallant, A.R., Hsieh, D.A., and Tauchen, G.E.On Fitting a Recalcitrant Series: The Pound/Dollar Exchange Rate, 1974–1983.” In Nonparametric and Semiparametric Methods in Economics and Statistics, edited by Barnett, W. A., Powell, J., and Tauchen, G. Cambridge: Cambridge University Press, 1991.Google Scholar
Gibbons, J.D. Nonparametric Statistical Inference. New York: Marcel Dekker, 1985.Google Scholar
Gong, B., and Sickles, R.Finite Sample Evidence on the Performance of Stochastic Frontiers and Data Envelopment Analysis Using Panel Data.” Journal of Econometrics 51 (1992):259–84.Google Scholar
Grabowski, R., and Pasurka, C.Farmer Education and Economic Efficiency: Northern Farms in 1860.” Economics Letters 28 (1988):315–20.Google Scholar
Grenander, U. Abstract Inference. New York: Wiley, 1981.Google Scholar
Grosskopf, S., and Hayes, K.Local Public Sector Bureaucrats and Their Input Choices.” Journal of Urban Economics (forthcoming).Google Scholar
Hall, B.F., and Leveen, E.P.Farm Size and Economic Efficiency: The Case of California.” American Journal of Agricultural Economics 60 (1978):589600.Google Scholar
Han, A.K.A Nonparametric Analysis of Transformations.” Journal of Econometrics 35 (1987a):191209.Google Scholar
Han, A.K.Nonparametric Analysis of a Generalized Regression Model.” Journal of Econometrics 35(1987b):303–16.Google Scholar
Hanoch, G., and Rothschild, M.Testing the Assumptions of Production Theory.” Journal of Political Economy 80 (1972):256–74.Google Scholar
Hardle, W. Applied Nonparametric Regression. Cambridge: Cambridge University Press, 1990.Google Scholar
Hardle, W., Hildenbrand, W., and Jerison, M.Empirical Evidence on the Law of Demand.” Econometrica 59 (1991):1525–50.Google Scholar
Holmes, J.M., and Hutton, P.A.On the Causal Relationship Between Government Expenditures and National Income.” Review of Economic Statistics 72 (1990):8795.Google Scholar
Holt, M.T., and Moschini, G.Alternative Measures of Risk in Commodity Supply Models: An Analysis of Sow Farrowing Decisions in the United States.” Journal of Agricultural and Resource Economics 17 (1992):112.Google Scholar
Hong, Y., and Pagan, A.Some Simulation Studies of Nonparametric Estimators.” Empirical Economics 13 (1988):251–66.Google Scholar
Horowitz, J.L.A Smoothed Maximum Score Estimator for the Binary Response Model.” Econometrica 60 (1992):505–32.Google Scholar
Hotelling, H., and Pabst, M.R.Rank Correlation and Tests of Significance Involving No Assumptions of Normality.” Annuals of Mathematical Statistics 7 (1936):2943.Google Scholar
Jondrow, J., Lovell, C.A. Knox, Materov, I.S., and Schmidt, P.On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model.” Journal of Econometrics 19 (1982):233–38.Google Scholar
Kendall, M.A New Measure of Rank Correlation.” Biometrika 30 (1938):8193.Google Scholar
Kendall, M. Rank Correlation Methods. London: Griffin, 1948.Google Scholar
Lovell, C.A. Knox, and Schmidt, P.A Comparison of Alternative Approaches to the Measurement of Productive Efficiency.” In Applications of Modern Production Theory: Efficiency and Productivity, edited by Dogramaci, A. and Färe, R. Boston: Kluwer Academic Publishers, 1988.Google Scholar
Kopp, R.J., and Diewert, W.E.The Decomposition of Frontier Cost Function Deviations into Measures of Technical and Allocative Efficiency.” Journal of Econometrics 19 (1982):319–31.Google Scholar
Lau, L.J.Applications of Duality Theory: A Comment.” In Frontiers of Quantitative Economics II, edited by Intriligator, M. and Kendrick, D. Amsterdam: North Holland, 1974.Google Scholar
Lee, L.Semiparametric Nonlinear Least Squares Estimation of Truncated Regression Models.” Econometric Theory 8 (1992):5294.Google Scholar
Lehmann, E.L. Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden-Day, 1975.Google Scholar
Lewin, A.Y., and Lovell, C.A. Knox, eds. “Frontier Analysis: Parametric and Nonparametric Approaches.” Journal of Econometrics 46(1990).Google Scholar
Maindiratta, A.Largest Size-Efficient Scale and Size Efficiencies of Decision-making Units in Data Envelopment Analysis.” Journal of Econometrics 46 (1990):5772.Google Scholar
Mann, H.B., and Whitney, D.R.On a Test of Whether One of Two Random Variables is Stochastically Larger than the Other.” Annuals of Mathematical Statistics 18 (1947):5060.Google Scholar
Manski, C.F.Adaptive Estimation of Nonlinear Regression Models.” Econometric Reviews 3 (1984):145–94.Google Scholar
Manski, C.F.Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator.” Journal of Econometrics 27 (1985):313–34.Google Scholar
Manski, C.F.Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data.” Econometrica 55 (1987):357–62.Google Scholar
Matzkin, R.L.A Nonparametric Rank Correlation Estimator.” In Nonparametric and Semiparametric Methods in Economics and Statistics, edited by Barnett, W. A., Powell, J., and Tauchen, G. Cambridge: Cambridge University Press, 1991a.Google Scholar
Matzkin, R.L.Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models.” Econometrica 59 (1991b):1315–28.Google Scholar
McCurdy, T.H., and Stengos, T.A Comparison of Risk-Premium Forecasts Implied by Parametric versus Nonparametric Conditional Mean Estimators.” Journal of Econometrics 52 (1992):225–44.Google Scholar
Meeusen, W., and van den Broeck, J.Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error.” International Economic Review 18 (1977):435–44.Google Scholar
Moschini, G.Nonparametric and Semiparametric Estimation: An Analysis of Multiproduct Returns to Scale.” American Journal of Agricultural Economics 72 (1990):589–96.Google Scholar
Moschini, G.Testing for Preference Change in Consumer Demand: An Indirectly Separable Semiparametric Model.” Journal of Business and Economic Statistics 9 (1991):111–17.Google Scholar
Nadaraya, E.A.On Estimating Regression.” Theory of Probability Applications 9(1964a):141–42.Google Scholar
Nadaraya, E.A.Some New Estimates for Distribution Functions.” Theory of Probability Applications 9(1964b):497500.Google Scholar
Newey, W.K.Adaptive Estimation of Regression Models via Moment Restrictions.” Journal of Econometrics 38 (1988):301–9.Google Scholar
Newey, W.K.Semiparametric Efficiency Bounds.” Journal of Applied Econometrics 5 (1990):99135.Google Scholar
Pagan, A.R., and Ullah, A.The Econometric Analysis of Models with Risk Terms.” Journal of Applied Econometrics 3 (1988):87105.Google Scholar
Pagan, A.R., and Schwert, G.W.Testing for Covariance Stationarity in Stock Market Data.” Economics Letters 33 (1990):165–70.Google Scholar
Pagan, A.R., and Wickens, M.R.A Survey of Some Recent Econometric Methods.” Economic Journal 99 (1989):9621025.Google Scholar
Pagan, A.R., and Hong, Y.S.Nonparametric Estimation and the Risk Premium.” In Nonparametric and Semiparametric Methods in Economics and Statistics, edited by Barnett, W.A., Powell, J., and Tauchen, G. Cambridge: Cambridge University Press, 1991.Google Scholar
Pope, R.D.Estimating Functional Forms with Special Reference to Agriculture: Comments.” American Journal of Agricultural Economics 66 (1984):223–24.Google Scholar
Pope, R.D., and Hallam, A.Separability Testing in Production Economics.” American Journal of Agricultural Economics 70 (1988):142–52.Google Scholar
Rao, B.L.S. Prakasa Nonparametric Functional Estimation. Orlando: Academic Press, 1983.Google Scholar
Randles, R.H., and Wolfe, D.A. Introduction to the Theory of Nonparametric Statistics. New York: Wiley, 1979.Google Scholar
Rangan, N., Grabowski, R., Aly, H.Y., and Pasurka, C.The Technical Efficiency of U.S. Banks.” Economics Letters 28 (1988):169–75.Google Scholar
Rilstone, P.Nonparametric Hypothesis Testing with Parametric Rates of Convergence.” International Economic Review 32 (1991):209–27.Google Scholar
Robinson, P.M.Nonparametric Estimators for Time Series.” Journal of Time Series Analysis 4 (1983):185207.Google Scholar
Robinson, P.M.Semiparametric Econometrics: A Survey.” Journal of Applied Econometrics 3 (1988):3551.Google Scholar
Robinson, P.M.Consistent Nonparametric Entropy-Based Testing.” Review of Economic Studies 58 (1991):437–53.Google Scholar
Rosenblatt, M.Remarks on Some Nonparametric Estimates of a Density Function.” Annuals of Mathematical Statistics 27 (1956):832–7.Google Scholar
Russell, R.R.Measures of Technical Efficiency.” Journal of Economic Theory 35 (1985):109–26.Google Scholar
Sakong, Y.Essays in Nonparametric Measures of Changes in Taste and Hedging Behavior with Options.” Ph.D. diss., Iowa State University, 1991.Google Scholar
Sakong, Y., and Hayes, D.J.A Test for the Consistency of Demand Data with Revealed Preference Theory.” American Journal of Agricultural Economics (forthcoming).Google Scholar
Schmidt, P.Frontier Production Functions.” Econometric Reviews 4 (1986):289328.Google Scholar
Schmidt, P., and Lovell, C.A. KnoxEstimating Technical and Allocative Inefficiency Relative to Stochastic Production and Cost Frontiers.” Journal of Econometrics 9 (1979):363–66.Google Scholar
Seiford, L.M., and Thrall, R.M.Recent Developments in Data Envelopment Analysis: The Mathematical Programming Approach to Frontier Analysis.” Journal of Econometrics 46 (1990):738.Google Scholar
Seitz, W.D.The Measurement of Efficiency Relative to a Frontier Production Function.” American Journal of Agricultural Economics 52 (1970):505–11.Google Scholar
Sengupta, J.K.Nonparametric Test of the Efficiency of Portfolio Investment.” Zeitschrift für Nationalolonomie 50 (1989):115.Google Scholar
Sentana, E., and Wadhwani, S.Semiparametric Estimation and the Predictability of Stock Market Returns: Some Lessons from Japan.” Review of Economic Studies 58 (1991):547–63.Google Scholar
Shephard, R.W. Indirect Production Functions. Mathematical Systems in Economics, no. 10. Meisenheim Am Glad: Verlag Anton Hain, 1974.Google Scholar
Silverman, B.W. Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall, 1986.Google Scholar
Stein, C.Efficient Nonparametric Testing and Estimation.” In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1956.Google Scholar
Stoker, T.M.Test of Additive Derivative Constraints.” Review of Economic Studies 56 (1989):535–52.Google Scholar
Stone, C.J.Adaptive Maximum Likelihood Estimation of a Location Parameter.” Annals of Statistics 3 (1975):267–84.Google Scholar
Timmer, C.P.Using a Probabilistic Frontier Production Function to Measure Technical Efficiency.” Journal of Political Economy 79 (1971):776–94.Google Scholar
Tolley, H.D., and Pope, R.D.Testing for Stochastic Dominance.” American Journal of Agricultural Economics 70 (1988):693700.Google Scholar
Tsur, Y.On Testing for Revealed Preference Conditions.” Economics Letters 31 (1989):359–62.Google Scholar
Ullah, A.Nonparametric Estimation of Econometric Functionals.” Canadian Journal of Economics 21 (1988):625–58.Google Scholar
Varian, H.R.The Nonparametric Approach to Demand Analysis.” Econometrica 50 (1982):945–73.Google Scholar
Varian, H.R.Nonparametric Tests of Consumer Behavior.” Review of Economic Studies 50(1983a):99110.Google Scholar
Varian, H.R.Nonparametric Tests of Models of Investor Behavior.” Journal of Financial and Quantitative Analysis 18(1983b):269–78.Google Scholar
Varian, H.R.The Nonparametric Approach to Production Analysis.” Econometrica 52 (1984):579–97.Google Scholar
Varian, H.R.Nonparametric Analysis of Optimizing Behavior with Measurement Error.” Journal of Econometrics 30 (1985):445–58.Google Scholar
Varian, H.R.Goodness of Fit in Optimizing Models.” Journal of Econometrics 46 (1990):125–40.Google Scholar
Vinod, H.D., and Ullah, A.Flexible Production Function Estimation by Nonparametric Kernel Estimators.” In Advances in Econometrics, vol. 7, edited by Rhodes, G.F. and Fomby, T.B. Greenwich: JAI Press, 1988.Google Scholar
Watson, G.S.Smooth Regression Analysis.” Sankhya Series A 26 (1964):359–72.Google Scholar
White, H., and Wooldridge, J.M.Some Results on Sieve Estimation with Dependent Observations.” In Nonparametric and Semiparametric Methods in Economics and Statistics, edited by Barnett, W.A., Powell, J., and Tauchen, G. Cambridge: Cambridge University Press, 1991.Google Scholar
Wilcoxin, F.Individual Comparisons by Ranking Methods.” Biometrics 1 (1945):8083.Google Scholar
Yatchew, A.Nonparametric Regression Model Tests Based on Least Squares.” Econometric Theory (forthcoming, 1992).Google Scholar
Zieschang, K.D.A Note on the Decomposition of Cost Efficiency into Technical and Allocative Components.” Journal of Econometrics 23 (1983):401–5.Google Scholar