48,293 research outputs found
Adaptive, Rate-Optimal Testing in Instrumental Variables Models
This paper proposes simple, data-driven, optimal rate-adaptive inferences on a structural function in semi-nonparametric conditional moment restrictions. We consider two types of hypothesis tests based on leave-one-out sieve estimators. A structure- space test (ST) uses a quadratic distance between the structural functions of endogenous variables; while an image-space test (IT) uses a quadratic distance of the conditional moment from zero. For both tests, we analyze their respective classes of nonparametric alternative models that are separated from the null hypothesis by the minimax rate of testing. That is, the sum of the type I and the type II errors of the test, uniformly over the class of nonparametric alternative models, cannot be improved by any other test. Our new minimax rate of ST diļ¬ers from the known minimax rate of estimation in nonparametric instrumental variables (NPIV) models. We propose computationally simple and novel exponential scan data-driven choices of sieve regularization parameters and adjusted chi-squared critical values. The resulting tests attain the minimax rate of testing, and hence optimally adapt to the unknown smoothness of functions and are robust to the unknown degree of ill-posedness (endogeneity). Data-driven conļ¬dence sets are easily obtained by inverting the adaptive ST. Monte Carlo studies demonstrate that our adaptive ST has good size and power properties in ļ¬nite samples for testing monotonicity or equality restrictions in NPIV models. Empirical applications to nonparametric multi-product demands with endogenous prices are presented
DATA-DRIVEN RATE-OPTIMAL SPECIFICATION TESTING IN REGRESSION MODELS
We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/\sqrt{n}. Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.Hypothesis testing, nonparametric adaptive tests, selection methods
Binscatter Regressions
We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg},
which implements the binscatter methods developed in
\citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the
commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}.
The first command (\texttt{binsreg}) implements binscatter for the regression
function and its derivatives, offering several point estimation, confidence
intervals and confidence bands procedures, with particular focus on
constructing binned scatter plots. The second command (\texttt{binsregtest})
implements hypothesis testing procedures for parametric specification and for
nonparametric shape restrictions of the unknown regression function. Finally,
the third command (\texttt{binsregselect}) implements data-driven number of
bins selectors for binscatter implementation using either quantile-spaced or
evenly-spaced binning/partitioning. All the commands allow for covariate
adjustment, smoothness restrictions, weighting and clustering, among other
features. A companion \texttt{R} package with the same capabilities is also
available
Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models
We propose a new adaptive hypothesis test for polyhedral cone (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modiļ¬ed leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve NPIV estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and adjusted chi-squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in L2. That is, the sum of its type I error uniformly over the composite null and its type II error uniformly over nonparametric alternative models cannot be improved by any other hypothesis test for NPIV models of unknown regularities. Data-driven confidence sets in L2 are obtained by inverting the adaptive test. Simulations con rm that our adaptive test controls size and its nite-sample power greatly exceeds existing non-adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented
Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models
We propose a new adaptive hypothesis test for polyhedral cone (e.g.,
monotonicity, convexity) and equality (e.g., parametric, semiparametric)
restrictions on a structural function in a nonparametric instrumental variables
(NPIV) model. Our test statistic is based on a modified leave-one-out sample
analog of a quadratic distance between the restricted and unrestricted sieve
NPIV estimators. We provide computationally simple, data-driven choices of
sieve tuning parameters and adjusted chi-squared critical values. Our test
adapts to the unknown smoothness of alternative functions in the presence of
unknown degree of endogeneity and unknown strength of the instruments. It
attains the adaptive minimax rate of testing in . That is, the sum of its
type I error uniformly over the composite null and its type II error uniformly
over nonparametric alternative models cannot be improved by any other
hypothesis test for NPIV models of unknown regularities. Data-driven confidence
sets in are obtained by inverting the adaptive test. Simulations confirm
that our adaptive test controls size and its finite-sample power greatly
exceeds existing non-adaptive tests for monotonicity and parametric
restrictions in NPIV models. Empirical applications to test for shape
restrictions of differentiated products demand and of Engel curves are
presented
Data-driven efficient score tests for deconvolution problems
We consider testing statistical hypotheses about densities of signals in
deconvolution models. A new approach to this problem is proposed. We
constructed score tests for the deconvolution with the known noise density and
efficient score tests for the case of unknown density. The tests are
incorporated with model selection rules to choose reasonable model dimensions
automatically by the data. Consistency of the tests is proved
Data-driven rate-optimal specification testing in regression models
We propose new data-driven smooth tests for a parametric regression function.
The smoothing parameter is selected through a new criterion that favors a large
smoothing parameter under the null hypothesis. The resulting test is adaptive
rate-optimal and consistent against Pitman local alternatives approaching the
parametric model at a rate arbitrarily close to 1/\sqrtn. Asymptotic critical
values come from the standard normal distribution and the bootstrap can be used
in small samples. A general formalization allows one to consider a large class
of linear smoothing methods, which can be tailored for detection of additive
alternatives.Comment: Published at http://dx.doi.org/10.1214/009053604000001200 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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