[
    {
        "id": "authors:9g8y6-hqs08",
        "collection": "authors",
        "collection_id": "9g8y6-hqs08",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160329-095921634",
        "type": "publication_workingpaper",
        "title": "Random Projection Estimation of Discrete-Choice Models With Large Choice Sets",
        "author": [
            {
                "family_name": "Chiong",
                "given_name": "Khai X.",
                "orcid": "0000-0002-6713-8907",
                "clpid": "Chiong-Khai-Xiang"
            },
            {
                "family_name": "Shum",
                "given_name": "Matthew",
                "orcid": "0000-0002-6262-915X",
                "clpid": "Shum-M"
            }
        ],
        "abstract": "We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, the high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclic monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semi-parametric and does not require explicit distributional assumptions to be made regarding the random utility errors. The random projection procedure is justified via the Johnson-Lindenstrauss Lemma: - the pairwise distances between data points are preserved during data compression, which we exploit to show convergence of our estimator. The estimator works well in a computational simulation and in a application to a supermarket scanner dataset.",
        "doi": "10.7907/9g8y6-hqs08",
        "publisher": "California Institute of Technology",
        "publication_date": "2016-03-29"
    },
    {
        "id": "authors:4gxmb-6an66",
        "collection": "authors",
        "collection_id": "4gxmb-6an66",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160329-093057029",
        "type": "publication_workingpaper",
        "title": "Duality in dynamic discrete choice models",
        "author": [
            {
                "family_name": "Chiong",
                "given_name": "Khai X.",
                "orcid": "0000-0002-6713-8907",
                "clpid": "Chiong-Khai-Xiang"
            },
            {
                "family_name": "Galichon",
                "given_name": "Alfred",
                "clpid": "Galichon-A"
            },
            {
                "family_name": "Shum",
                "given_name": "Matthew",
                "orcid": "0000-0002-6262-915X",
                "clpid": "Shum-M"
            }
        ],
        "abstract": "Using results from convex analysis, we investigate a novel approach to identification and estimation of discrete choice models which we call the \"Mass Transport Approach\" (MTA). We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program which is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of convex-analytic tools to dynamic discrete choice models, and the connection with two-sided matching models, is new in the literature.",
        "doi": "10.7907/4gxmb-6an66",
        "publisher": "California Institute of Technology",
        "publication_date": "2015-02"
    },
    {
        "id": "authors:vgp0z-00y54",
        "collection": "authors",
        "collection_id": "vgp0z-00y54",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170727-090045366",
        "type": "publication_workingpaper",
        "title": "Estimating Dynamic Discrete Choice Models Via Convex Analysis",
        "author": [
            {
                "family_name": "Chiong",
                "given_name": "Khai X.",
                "orcid": "0000-0002-6713-8907",
                "clpid": "Chiong-Khai-Xiang"
            },
            {
                "family_name": "Galichon",
                "given_name": "Alfred",
                "clpid": "Galichon-A"
            },
            {
                "family_name": "Shum",
                "given_name": "Matthew",
                "orcid": "0000-0002-6262-915X",
                "clpid": "Shum-M"
            }
        ],
        "abstract": "Using results from convex analysis, we characterize the identification and estimation of dynamic discrete-choice models based on the random utility framework. Based on these insights, we propose a new two-step estimator for these models, which is easily applicable to models in which the utility shocks may not derive from an extreme- value distribution, and may be mutually correlated with each other and with the state variables. Monte Carlo results demonstrate the good performance of this estimator, and we provide a short application using the dynamic bus engine replacement model in Rust (1987).",
        "doi": "10.7907/vgp0z-00y54",
        "publisher": "California Institute of Technology",
        "publication_date": "2013-05"
    }
]