A class of smooth estimators for discrete distributions

Wang, Min-Chiang; Ryzin, John Van

doi:10.1093/biomet/68.1.301

Cited by 123 publications

(28 citation statements)

References 12 publications

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“…In the ordered case, alternative approaches can be used, employing in effect near-neighbour weights. See, for example, Wang and van Ryzin (1981), Burman (1987) and Hall and Titterington (1987).…”

Section: Methodology For Cross-validationmentioning

confidence: 99%

Cross-Validation and the Estimation of Conditional Probability Densities

Hall

Racine

2004

Journal of the American Statistical Association

399

306

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ABSTRACT. Many practical problems, especially some connected with forecasting, require nonparametric estimation of conditional densities from mixed data. For example, given an explanatory data vector X for a prospective customer, with components that could include the customer's salary, occupation, age, sex, marital status and address, a company might wish to estimate the density of the expenditure, Y , that could be made by that person, basing the inference on observations of (X, Y ) for previous clients. Choosing appropriate smoothing parameters for this problem can be tricky, not least because plug-in rules take a particularly complex form in the case of mixed data. An obvious difficulty is that there exists no general formula for the optimal smoothing parameters. More insidiously, and more seriously, it can be difficult to determine which components of X are relevant to the problem of conditional inference. For example, if the jth component of X is independent of Y then that component is irrelevant to estimating the density of Y given X, and ideally should be dropped before conducting inference. In this paper we show that cross-validation overcomes these difficulties. It automatically determines which components are relevant and which are not, through assigning large smoothing parameters to the latter and consequently shrinking them towards the uniform distribution on the respective marginals. This effectively removes irrelevant components from contention, by suppressing their contribution to estimator variance; they already have very small bias, a consequence of their independence of Y . Crossvalidation also gives us important information about which components are relevant: the relevant components are precisely those which cross-validation has chosen to smooth in a traditional way, by assigning them smoothing parameters of conventional size. Indeed, cross-validation produces asymptotically optimal smoothing for relevant components, while eliminating irrelevant components by oversmoothing. In the problem of nonparametric estimation of a conditional density, cross-validation comes into its own as a method with no obvious peers.

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Section: Methodology For Cross-validationmentioning

confidence: 99%

Cross-Validation and the Estimation of Conditional Probability Densities

Hall

Racine

2004

Journal of the American Statistical Association

399

306

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“…K(·) now denotes a product kernel (i.e., the product of several kernel functions), because X is multidimensional. For continuous elements in X, the Epanechnikov kernel is used, while for ordered and unordered discrete regressors, the kernel functions are based on Wang and van Ryzin (1981) and Aitchison and Aitken (1976), respectively. The bandwidth h is selected via Kullback-Leibler cross-validation, see Hurvich, Simonoff, and Tsai (1998).…”

Section: Nonparametric Estimation Of the Propensity Scorementioning

confidence: 99%

The finite sample performance of semi- and non-parametric estimators for treatment effects and policy evaluation

Frölich

Huber

Wiesenfarth

2017

Computational Statistics & Data Analysis

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This paper investigates the finite sample performance of a comprehensive set of semi-and nonparametric estimators for treatment and policy evaluation. In contrast to previous simulation studies which mostly considered semiparametric approaches relying on parametric propensity score estimation, we also consider more flexible approaches based on semi-or nonparametric propensity scores, nonparametric regression, and direct covariate matching. In addition to (pair, radius, and kernel) matching, inverse probability weighting, regression, and doubly robust estimation, our studies also cover recently proposed estimators such as genetic matching, entropy balancing, and empirical likelihood estimation. We vary a range of features (sample size, selection into treatment, effect heterogeneity, and correct/misspecification) in our simulations and find that several nonparametric estimators by and large outperform commonly used treatment estimators using a parametric propensity score. Nonparametric regression, nonparametric doubly robust estimation, nonparametric IPW, and one-to-many covariate matching perform best.

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“…9 While the kernels for ordered categorical variables of Wang and van Ryzin (1981) and Racine and Li (2004) are clearly different, the kernels for unordered categorical variables of Aitchison and Aitken (1976) and Li and Racine (2004) have exactly the same shape, but a different specification of the bandwidth parameter so that the choice between the kernels for unordered categorical variables does not make a difference if the bandwidth parameters are appropriately adjusted, e.g. by data-driven bandwidth selection (Czekaj and Henningsen, 2013).…”

Section: Econometric Specificationmentioning

confidence: 99%

Transaction costs and social networks in productivity measurement

Henningsen

Henning

2014

Empir Econ

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We argue that in the presence of transaction costs, observed productivity measures may in many cases understate the true productivity, as production data seldom distinguish between resources entering the production process and resources of a similar type that are sacrificed for transaction costs. Hence, both the absolute productivity measures and, more importantly, the productivity ranking will be distorted. A major driver of transaction costs is poor access to information and contract enforcement assistance. Social networks often catalyse information exchange as well as generate trust and support. Hence, we use measures of a firm's access to social networks as a proxy for the transaction costs the firm faces. We develop a microeconomic production model that takes into account transaction costs and networks. Using a data set of 384 Polish farms, we empirically estimate this model and compare different parametric, semiparametric, and nonparametric model specifications. Our results generally support our hypothesis. Especially large trading networks and dense household networks have a positive influence on a farm's productivity. Furthermore, our results indicate that transaction costs have a measurable impact on the productivity ranking of the farms.

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A class of smooth estimators for discrete distributions

Cited by 123 publications

References 12 publications

Cross-Validation and the Estimation of Conditional Probability Densities

Cross-Validation and the Estimation of Conditional Probability Densities

The finite sample performance of semi- and non-parametric estimators for treatment effects and policy evaluation

Transaction costs and social networks in productivity measurement

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