289,155 research outputs found
nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference
Nonparametric kernel density and local polynomial regression estimators are very popular in statistics, economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as a preliminary ingredient entering some other estimation or inference procedure. This article describes the main methodological and numerical features of the software package nprobust, which offers an array of estimation and inference procedures for nonparametric kernel-based density and local polynomial regression methods, implemented in both the R and Stata statistical platforms. The package includes not only classical bandwidth selection, estimation, and inference methods (Wand and Jones 1995; Fan and Gijbels 1996), but also other recent developments in the statistics and econometrics literatures such as robust bias-corrected inference and coverage error optimal bandwidth selection (Calonico, Cattaneo, and Farrell 2018, 2019a). Furthermore, this article also proposes a simple way of estimating optimal bandwidths in practice that always delivers the optimal mean square error convergence rate regardless of the specific evaluation point, that is, no matter whether it is implemented at a boundary or interior point. Numerical performance is illustrated using an empirical application and simulated data, where a detailed numerical comparison with other R packages is given
nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference
Nonparametric kernel density and local polynomial regression estimators are
very popular in Statistics, Economics, and many other disciplines. They are
routinely employed in applied work, either as part of the main empirical
analysis or as a preliminary ingredient entering some other estimation or
inference procedure. This article describes the main methodological and
numerical features of the software package nprobust, which offers an array of
estimation and inference procedures for nonparametric kernel-based density and
local polynomial regression methods, implemented in both the R and Stata
statistical platforms. The package includes not only classical bandwidth
selection, estimation, and inference methods (Wand and Jones, 1995; Fan and
Gijbels, 1996), but also other recent developments in the statistics and
econometrics literatures such as robust bias-corrected inference and coverage
error optimal bandwidth selection (Calonico, Cattaneo and Farrell, 2018, 2019).
Furthermore, this article also proposes a simple way of estimating optimal
bandwidths in practice that always delivers the optimal mean square error
convergence rate regardless of the specific evaluation point, that is, no
matter whether it is implemented at a boundary or interior point. Numerical
performance is illustrated using an empirical application and simulated data,
where a detailed numerical comparison with other R packages is given
Uniform Inference for Kernel Density Estimators with Dyadic Data
Dyadic data is often encountered when quantities of interest are associated
with the edges of a network. As such it plays an important role in statistics,
econometrics and many other data science disciplines. We consider the problem
of uniformly estimating a dyadic Lebesgue density function, focusing on
nonparametric kernel-based estimators taking the form of dyadic empirical
processes. Our main contributions include the minimax-optimal uniform
convergence rate of the dyadic kernel density estimator, along with strong
approximation results for the associated standardized and Studentized
-processes. A consistent variance estimator enables the construction of
valid and feasible uniform confidence bands for the unknown density function.
We showcase the broad applicability of our results by developing novel
counterfactual density estimation and inference methodology for dyadic data,
which can be used for causal inference and program evaluation. A crucial
feature of dyadic distributions is that they may be "degenerate" at certain
points in the support of the data, a property making our analysis somewhat
delicate. Nonetheless our methods for uniform inference remain robust to the
potential presence of such points. For implementation purposes, we discuss
inference procedures based on positive semi-definite covariance estimators,
mean squared error optimal bandwidth selectors and robust bias correction
techniques. We illustrate the empirical finite-sample performance of our
methods both in simulations and with real-world trade data, for which we make
comparisons between observed and counterfactual trade distributions in
different years. Our technical results concerning strong approximations and
maximal inequalities are of potential independent interest.Comment: Article: 23 pages, 3 figures. Supplemental appendix: 72 pages, 3
figure
New estimators of the Bayes factor for models with high-dimensional parameter and/or latent variable spaces
Formal Bayesian comparison of two competing models, based on the posterior odds ratio, amounts to estimation of the Bayes factor, which is equal to the ratio of respective two marginal data density values. In models with a large number of parameters and/or latent variables, they are expressed by high-dimensional integrals, which are often computationally infeasible. Therefore, other methods of evaluation of the Bayes factor are needed. In this paper, a new method of estimation of the Bayes factor is proposed. Simulation examples confirm good performance of the proposed estimators. Finally, these new estimators are used to formally compare different hybrid Multivariate Stochastic Volatility–Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MSV-MGARCH) models which have a large number of latent variables. The empirical results show, among other things, that the validity of reduction of the hybrid MSV-MGARCH model to the MGARCH specification depends on the analyzed data set as well as on prior assumptions about model parameters
Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution
Value at Risk (VaR) forecasts can be produced from conditional autoregressive VaR models, estimated using quantile regression. Quantile modeling avoids a distributional assumption, and allows the dynamics of the quantiles to differ for each probability level. However, by focusing on a quantile, these models provide no information regarding Expected Shortfall (ES), which is the expectation of the exceedances beyond the quantile. We introduce a method for predicting ES corresponding to VaR forecasts produced by quantile regression models. It is well known that quantile regression is equivalent to maximum likelihood based on an asymmetric Laplace (AL) density. We allow the density’s scale to be time-varying, and show that it can be used to estimate conditional ES. This enables a joint model of conditional VaR and ES to be estimated by maximizing an AL log-likelihood. Although this estimation framework uses an AL density, it does not rely on an assumption for the returns distribution. We also use the AL log-likelihood for forecast evaluation, and show that it is strictly consistent for the joint evaluation of VaR and ES. Empirical illustration is provided using stock index data
Neural parameters estimation for brain tumor growth modeling
Understanding the dynamics of brain tumor progression is essential for
optimal treatment planning. Cast in a mathematical formulation, it is typically
viewed as evaluation of a system of partial differential equations, wherein the
physiological processes that govern the growth of the tumor are considered. To
personalize the model, i.e. find a relevant set of parameters, with respect to
the tumor dynamics of a particular patient, the model is informed from
empirical data, e.g., medical images obtained from diagnostic modalities, such
as magnetic-resonance imaging. Existing model-observation coupling schemes
require a large number of forward integrations of the biophysical model and
rely on simplifying assumption on the functional form, linking the output of
the model with the image information. In this work, we propose a learning-based
technique for the estimation of tumor growth model parameters from medical
scans. The technique allows for explicit evaluation of the posterior
distribution of the parameters by sequentially training a mixture-density
network, relaxing the constraint on the functional form and reducing the number
of samples necessary to propagate through the forward model for the estimation.
We test the method on synthetic and real scans of rats injected with brain
tumors to calibrate the model and to predict tumor progression
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