Simple and Honest Confidence Intervals in Nonparametric Regression

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 that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n^{−4/5}, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in an empirical application

Simple and Honest Confidence Intervals in Nonparametric Regression

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 that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n -4/5 , the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in an empirical application

Simple and Honest Confidence Intervals in Nonparametric Regression

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 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 that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n^{−2/5}, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in a Monte Carlo analysis and an empirical application

Bayes and empirical Bayes: do they merge?

Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach, plugging empirical estimates of the prior hyperparameters into the posterior distribution. Even if not rigorously justified, the underlying idea is that, when the sample size is large, empirical Bayes leads to "similar" inferential answers. Yet, precise mathematical results seem to be missing. In this work, we give a more rigorous justification in terms of merging of Bayes and empirical Bayes posterior distributions. We consider two notions of merging: Bayesian weak merging and frequentist merging in total variation. Since weak merging is related to consistency, we provide sufficient conditions for consistency of empirical Bayes posteriors. Also, we show that, under regularity conditions, the empirical Bayes procedure asymptotically selects the value of the hyperparameter for which the prior mostly favors the "truth". Examples include empirical Bayes density estimation with Dirichlet process mixtures.Comment: 27 page

Simple and Honest Confidence Intervals in Nonparametric Regression

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 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 that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n^{-2/5}, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in a Monte Carlo analysis and an empirical application

Access to Substance Abuse Treatment in Western Kentucky

Abstract Substance abuse in Western Kentucky has reached near epidemic proportions. One of the major concerns for this epidemic is limited access to treatment. Although access to treatment in Western Kentucky may be limited, the region offers many different treatment options. This manual will help each individual to take an honest look at their drinking and drug use, assist them into entering a treatment facility, and provide long term treatment alternatives to help obtain sobriety. Recovery is a way of life and results vary for each person and are dependent upon their efforts to change their entire way of life. This guide will give those affected a hope for freedom and many healthy alternatives to substance abuse

Kompetensi Sosial Guru Mata Pelajaran Sosiologi dalam Bersikap Inklusif di Kelas XI IPS 1 Madrasah Aliyah Negeri 2 Pontianak

The purpose of this research is to find out sociology teacher's social competency in behaving inclusive with students class XI IPS 1 Madrasah Aliyah Negeri 2 Pontianak. The approach of this research is qualitative approach with descriptive method. The research result shows that the sociology teacher's social competency in behaving open towards students classified as good. Open behavior is showed by teacher through honest attitude, humble and fair towards students when learning activity was take placed in class. The sociology teacher's ability in communicating dialogic is also classified as good, this is showed by teacher when the discussion with students take places in class, thus after the teacher present the material, students are gave the opportunity first in questioning something connected to the material which is learnt, after that students give the opportunity to students who deserve to answer the question which is presented by friends, and the last, from the question and answer which are presented by students, teacher responses and gives the summary totality

Doctoral supervisors and PhD students' perceptions about the supervision process in a young European university

In the last decade with the Bologna implementation, doctoral supervision gained a new emphasis and emerged as crucial for developing the European research area. Research, on doctoral supervision practices, and the supervisor ideal profile was carried out in a TOP 10 young European university, at Universidade Nova de Lisboa. The results show that meetings (individual or in groups) are the most implemented practice. Usually, students present orally, to a supervisor, the research that they already made regarding the initial work plane. Two supervisors’ profiles emerge from the students’ voices, the real and the ideal. The ideal supervisor profile that emerges from the questionnaires features supervisors who take students care, give feedback on work on time, and are honest and critical.publishersversionpublishe

Debating Immigration Restriction: the Case for Low and Slow

This article critiques our current politics of immigration, which is dominated by moralized and sentimental rhetoric. It argues for a more honest and balanced discussion of the merits of the status quo. A more mature debate would take into account many factors that now receive insufficient attention from politicians, academics, and the mainstream media, including the interests of voters and citizens as well as newcomers, legitimate nationalistic concerns both economic and cultural, the need for unity, stability, and cohesion through assimilation to a common culture, the primacy of American sovereignty through the maintenance of secure borders, and the integrity of the rule of law, which mandates the consistent enforcement of democratically enacted immigration laws. It should be incumbent on all sides to generate concrete reform proposals that give weight to all these concerns