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Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models

Author

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  • Kosaku Takanashi

    (Faculty of Economics, Keio University)

Abstract

We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In the above circumstance, narrow convergence with respect to uniform convergence fails to hold, because of the strength of it's topology. A new approach we propose to the lack-of-uniform-convergence is based on Mosco-convergence that is weaker topology than uniform convergence. By applying narrow convergence with respect to Mosco topology, we develop an infinite-dimensional version of the convexity argument and provide a proof of a local asymptotic normality. Our new technique also provides a proof of an asymptotic distribution of the likelihood ratio test statistic defined on real separable Hilbert spaces.

Suggested Citation

  • Kosaku Takanashi, 2017. "Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models," Keio-IES Discussion Paper Series 2017-012, Institute for Economics Studies, Keio University.
    • Handle: RePEc:keo:dpaper:2017-012
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    References listed on IDEAS

    as
    1. Bucher, Axel & Segers, Johan & Volgushev, Stanislav, 2014. "When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs," LIDAM Reprints ISBA 2014018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    3. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    4. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Epi-convergence; Likelihood ratio test; Local asymptotic normality; Mosco-topology;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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