Open Access. Powered by Scholars. Published by Universities.®
Social and Behavioral Sciences Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 12 of 12
Full-Text Articles in Social and Behavioral Sciences
Adaptation Bounds For Confidence Bands Under Self-Similarity, Timothy B. Armstrong
Adaptation Bounds For Confidence Bands Under Self-Similarity, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine and Nickl (2010). We find that adaptation can only be achieved up to a term that depends on the choice of the constant used to define self-similarity, and that this term becomes arbitrarily large for conservative choices of the self-similarity constant. We construct a confidence band that achieves this bound, up to a constant term that does not depend on the …
Adaptation Bounds For Confidence Bands Under Self-Similarity, Timothy B. Armstrong
Adaptation Bounds For Confidence Bands Under Self-Similarity, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine and Nickl (2010). We find that adaptation can only be achieved up to a term that depends on the choice of the constant used to define self-similarity, and that this term becomes arbitrarily large for conservative choices of the self-similarity constant. We construct a confidence band that achieves this bound, up to a constant term that does not depend on the …
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean-squared error results in CIs that are nearly efficient and …
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum meansquared error results in CIs that are nearly efficient and …
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive …
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive the optimal …
Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár
Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is …
Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár
Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is …
Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár
Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is …
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.