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Minimax Testing of a Composite null Hypothesis Defined via a Quadratic Functional in the Model of regression

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Author Info

  • Laetitia Comminges

    ()
    (CREST)

  • Arnak Dalalyan

    ()
    (LIGM/IMAGINE)

Abstract

We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional Q, the null hypothesis states that the regression function f satisfies the constraint Q[f] = 0, while the alternative corresponds to the functions for which Q[f] is bounded away from zero. On the one hand, we provide minimax rates of testing and the exact separation constants, along with a sharp-optimal testing procedure, for diagonal and nonnegative quadratic functionals. We consider smoothness classes of ellipsoidal form and check that our conditions are fulfilled in the particular case of ellipsoids corresponding to anisotropic Sobolev classes. In this case, we present a closed form of the minimax rate and the separation constant. On the other hand, minimax rates for quadratic functionals which are neither positive nor negative makes appear two different regimes: “regular" and “irregular". In the “regular" case, the minimax rate is equal to n-1/4 while in the “irregular" case, the rate depends on the smoothness class and is slower than in the “regular" case. We apply this to the issue of testing the equality of norms of two functions observed in noisy environments

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2012-19.

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Length: 37
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Handle: RePEc:crs:wpaper:2012-19

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Related research

Keywords: Nonparametric hypotheses testing; Sharp asymptotics; separation rates; Minimax approach; High-dimensional regression;

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  1. Philipp Kircher & Iourii Manovski & Fane Nadja Groes, 2009. "The U-Shapes of Occupational Mobility," 2009 Meeting Papers 26, Society for Economic Dynamics.
  2. Bartel, Ann P & Lichtenberg, Frank R, 1987. "The Comparative Advantage of Educated Workers in Implementing New Technology," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 1-11, February.
  3. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Wiley Blackwell, vol. 38(114), pages 175-208, April.
  4. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-24, September.
  5. Jean-Marc Robin, 2011. "On the Dynamics of unemployment and wage Distributions," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  6. Galor, Oded & Tsiddon, Daniel, 1997. "Technological Progress, Mobility, and Economic Growth," American Economic Review, American Economic Association, vol. 87(3), pages 363-82, June.
  7. Wojciech Kopczuk & Emmanuel Saez & Jae Song, 2010. "Earnings Inequality and Mobility in the United States: Evidence from Social Security Data since 1937," The Quarterly Journal of Economics, MIT Press, vol. 125(1), pages 91-128, February.
  8. Garcia-Penalosa, Cecilia & Aghion, Philippe & Caroli, Eve, 1999. "Inequality and Economic Growth: The Perspective of the New Growth Theories," Economics Papers from University Paris Dauphine 123456789/10091, Paris Dauphine University.
  9. Simon Beck & Thierry Kamionka, 2012. "Mobilités, inégalités et trajectoires professionnelles," Revue économique, Presses de Sciences-Po, vol. 63(3), pages 453-464.
  10. Pauline GIVORD & Lionel WILNER, 2009. "Fixed-Term Contracts, Incentives and Effort," Working Papers 2009-15, Centre de Recherche en Economie et Statistique.
  11. Donghoon Lee & Kenneth I. Wolpin, 2004. "Intersectoral Labor Mobility and the Growth of the Service Sector," PIER Working Paper Archive 04-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  12. Cecilia Garcia-Penalosa & Eve Caroli & Philippe Aghion, 1999. "Inequality and Economic Growth: The Perspective of the New Growth Theories," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1615-1660, December.
  13. Guasch, Jose Luis & Laffont, Jean-Jacques & Straub, Stéphane, 2005. "Concessions of Infrastructure in Latin America: Goverment-Led Renegotiation," IDEI Working Papers 372, Institut d'Économie Industrielle (IDEI), Toulouse.
  14. Cowell, Frank A, 1985. "Measures of Distributional Change: An Axiomatic Approach," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 135-51, January.
  15. François Bourguignon & Christian Morrisson, 2002. "Inequality Among World Citizens: 1820-1992," American Economic Review, American Economic Association, vol. 92(4), pages 727-744, September.
  16. Jolivet, Gregory & Postel-Vinay, Fabien & Robin, Jean-Marc, 2006. "The empirical content of the job search model: Labor mobility and wage distributions in Europe and the US," European Economic Review, Elsevier, vol. 50(4), pages 877-907, May.
  17. Anthony B. Atkinson & Thomas Piketty & Emmanuel Saez, 2009. "Top Incomes in the Long Run of History," NBER Working Papers 15408, National Bureau of Economic Research, Inc.
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