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Marco Avellamedina - One of the best experts on this subject based on the ideXlab platform.

  • privacy preserving Parametric Inference a case for robust statistics
    Journal of the American Statistical Association, 2019
    Co-Authors: Marco Avellamedina
    Abstract:

    AbstractDifferential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine le...

  • privacy preserving Parametric Inference a case for robust statistics
    arXiv: Learning, 2019
    Co-Authors: Marco Avellamedina
    Abstract:

    Differential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine learning. In this paradigm one assumes there is a trusted curator who holds the data of individuals in a database and the goal of privacy is to simultaneously protect individual data while allowing the release of global characteristics of the database. In this setting we introduce a general framework for Parametric Inference with differential privacy guarantees. We first obtain differentially private estimators based on bounded influence M-estimators by leveraging their gross-error sensitivity in the calibration of a noise term added to them in order to ensure privacy. We then show how a similar construction can also be applied to construct differentially private test statistics analogous to the Wald, score and likelihood ratio tests. We provide statistical guarantees for all our proposals via an asymptotic analysis. An interesting consequence of our results is to further clarify the connection between differential privacy and robust statistics. In particular, we demonstrate that differential privacy is a weaker stability requirement than infinitesimal robustness, and show that robust M-estimators can be easily randomized in order to guarantee both differential privacy and robustness towards the presence of contaminated data. We illustrate our results both on simulated and real data.

Viktor Todorov - One of the best experts on this subject based on the ideXlab platform.

  • Parametric Inference and dynamic state recovery from option panels
    Econometrica, 2015
    Co-Authors: Torben G Andersen, Nicola Fusari, Viktor Todorov
    Abstract:

    We develop a new Parametric estimation procedure for option panels observed with error. We exploit asymptotic approximations assuming an ever increasing set of option prices in the moneyness (cross‐sectional) dimension, but with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estimators converge stably to a mixed‐Gaussian law and we develop feasible estimators for the limiting variance. We also provide semiParametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and one constructed nonParametrically from high‐frequency data on the underlying asset. Furthermore, we develop new tests for the day‐by‐day model fit over specific regions of the volatility surface and for the stability of the risk‐neutral dynamics over time. A comprehensive Monte Carlo study indicates that the Inference procedures work well in empirically realistic settings. In an empirical application to S&P 500 index options, guided by the new diagnostic tests, we extend existing asset pricing models by allowing for a flexible dynamic relation between volatility and priced jump tail risk. Importantly, we document that the priced jump tail risk typically responds in a more pronounced and persistent manner than volatility to large negative market shocks.

  • Parametric Inference and dynamic state recovery from option panels
    National Bureau of Economic Research, 2012
    Co-Authors: Torben G Andersen, Nicola Fusari, Viktor Todorov
    Abstract:

    We develop a new Parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness- maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semiParametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained nonParametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model fit for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time. A large-scale Monte Carlo study indicates the Inference procedures work well for empirically realistic specifications and sample sizes. In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying jump risk premia and a flexible relation between risk premia and the level of risk. Both extensions lead to an improved characterization of observed option prices.

  • Parametric Inference and dynamic state recovery from option panels
    CREATES Research Papers, 2011
    Co-Authors: Torben G Andersen, Nicola Fusari, Viktor Todorov
    Abstract:

    We develop a new Parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness-maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semiParametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained nonParametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model t for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time. A large-scale Monte Carlo study indicates that the Inference procedures work well for empirically realistic model specifications and sample sizes. In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying risk premia of extreme events, i.e., jumps, as well as a more exible relation between the risk premia and the level of risk. We show that both extensions provide a significantly improved characterization, both statistically and economically, of observed option prices.

Geert Ridder - One of the best experts on this subject based on the ideXlab platform.

  • three stage semi Parametric Inference control variables and differentiability
    Journal of Econometrics, 2019
    Co-Authors: Jinyong Hahn, Geert Ridder
    Abstract:

    We show the usefulness of the path-derivative calculations that were introduced in econometrics by Newey (1994) for multi-step semi-Parametric estimators. These estimators estimate a finite-dimensional parameter using moment conditions that depend on nonParametric regressions on observed and estimated regressors that are estimated in the second and first step of the estimation procedure, respectively. Our earlier paper showed that Newey’s calculations can be extended to three-step estimators. In the current paper we consider the control variable (CV) estimator and related statistics in semi-Parametric econometric models with non-separable errors and regressors that are correlated with these errors. Non-separable econometric models with endogenous regressors are often identified by average moment restrictions that average over control variables, and these control variables are estimated in a first stage by (non)Parametric regression. We study aspects of Inference for such estimators where we focus on a finite-dimensional parameter vector or statistic. The asymptotic distribution and a closed-form expression for the asymptotic variance of the CV estimator were not available until now. Our path derivative calculations are much simpler than the derivation of the asymptotic distribution by a stochastic expansion that is particularly complicated for multi-step semi-Parametric estimators. We also consider just- and overidentification of the parameters and we propose a diagnostic test for overidentifying restrictions in models with non-separable errors and endogenous regressors. Finally, the path-derivative calculation breaks down if the moment condition is not differentiable. In an example we show that non-differentiability is associated with irregular behavior of the estimator.

  • three stage semi Parametric Inference control variables and differentiability
    2016
    Co-Authors: Jinyong Hahn, Geert Ridder
    Abstract:

    We show the usefulness of the path-derivative calculations that were introduced in econometrics by Newey (1994) for multi-step semi-Parametric estimators. These estimators estimate a finite-dimensional parameter using moment conditions that depend on nonParametric regressions on observed and estimated regressors that are estimated in the second and first step of the estimation procedure, respectively. Our earlier paper showed that Newey's calculations can be extended to three-step estimators. In the current paper we consider the control variable (CV) estimator and related statistics in semi-Parametric econometric models with non-separable errors and regressors that are correlated with these errors. Non-separable econometric models with endogenous regressors are often identified by average moment restrictions that average over control variables, and these control variables are estimated in a first stage by (non)Parametric regression. We study aspects of Inference for such estimators where we focus on a finite-dimensional parameter vector or statistic. The asymptotic distribution and a closed-form expression for the asymptotic variance of the CV estimator were not available until now. Our path derivative calculations are much simpler than the derivation of the asymptotic distribution by a stochastic expansion that is particularly complicated for multi-step semiParametric estimators. We also consider just and over identification of the parameters. This allows us to propose a diagnostic test for overidentifying restrictions in models with non-separable errors and endogenous regressors. Finally, the path-derivative calculation breaks down if the moment condition is not differentiable. In an example we show that non-difierentiability is associated with irregular behavior of the estimator.

Alessandra Rosalba Brazzale - One of the best experts on this subject based on the ideXlab platform.

  • Accurate Parametric Inference for Small Samples
    Statistical Science, 2008
    Co-Authors: Alessandra Rosalba Brazzale, Anthony C. Davison
    Abstract:

    We outline how modern likelihood theory, which provides essentially exact Inferences in a variety of Parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical asymptotic approximations, the focus of this paper is not on theory but on implementation and applications. Numerical illustrations are given for logistic regression, nonlinear models, and linear non-normal models, and we describe a sampling approach for the third of these classes. In the case of logistic regression, we argue that approximations are often more appropriate than `exact' procedures, even when these exist.

  • Practical small-sample Parametric Inference
    2000
    Co-Authors: Alessandra Rosalba Brazzale
    Abstract:

    These Ecole polytechnique federale de Lausanne EPFL, n° 2230 (2000)Faculte des sciences de baseInstitut de mathematiquesChaire de statistiqueJury: Robert Dalang, Thomas Diciccio, Stephan Morgenthaler, Ib Skovgaard Public defense: 2000-9-1 Reference doi:10.5075/epfl-thesis-2230Print copy in library catalog Record created on 2005-03-16, modified on 2017-05-12

Narayanaswamy Balakrishnan - One of the best experts on this subject based on the ideXlab platform.

  • Pooled Parametric Inference for minimal repair systems
    Computational Statistics, 2015
    Co-Authors: Morteza Amini, Narayanaswamy Balakrishnan
    Abstract:

    Consider two independent and identically structured systems, each with a certain number of observed repair times. The repair process is assumed to be performed according to a minimal-repair strategy. In this strategy, the state of the system after the repair is the same as it was immediately before the failure of the system. The resulting pooled sample is then used to obtain best linear unbiased estimators (BLUEs) as well as best linear invariant estimators of the location and scale parameters of the presumed Parametric families of life distributions. It is observed that the BLUEs based on the pooled sample are overall more efficient than those based on one sample of the same size and also than those based on independent samples. Furthermore, the best linear unbiased predictor and the best linear invariant predictor of a future repair time from an independent system are also obtained. A real data set of Boeing air conditioners, consisting of successive failures of the air conditioning system of each member of a fleet of Boeing jet airplanes, is used to illustrate the inferential results developed here.

  • Progressive Type-I Interval Censored Data
    The Art of Progressive Censoring, 2014
    Co-Authors: Narayanaswamy Balakrishnan, Erhard Cramer
    Abstract:

    Inference for progressive Type-I interval censored data is presented. The discussion includes Parametric Inference as well as problems of choosing optimal inspection times and optimal progressive interval censoring proportions.

  • A Meta-Analysis of Multisample Type-II Censored Data With Parametric and NonParametric Results
    IEEE Transactions on Reliability, 2013
    Co-Authors: Narayanaswamy Balakrishnan, William Volterman, Li Zhang
    Abstract:

    We discuss meta-analysis of multiple s-independent Type-II right censored data. In particular, we consider Parametric Inference using Best Linear Unbiased Estimation, as well as non-Parametric Inference. We provide pertinent numerical results and two examples to illustrate all the methods of Inference developed here.