Bootstrap Standard Error Estimates and Inference

Econometrica ◽  
2021 ◽  
Vol 89 (4) ◽  
pp. 1963-1977 ◽  
Author(s):  
Jinyong Hahn ◽  
Zhipeng Liao
Keyword(s):  
Weak Convergence ◽  
Error Estimates ◽  
Limit Distribution ◽  
Standard Error ◽  
Asymptotic Variance ◽  
Theory And Practice ◽  
Second Moment ◽  
Theoretical Literature ◽  
Bootstrap Distribution

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

Bootstrapping Quantile Regression Estimators

1995 ◽  
Vol 11 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
Quantile Regression ◽  
Limit Distribution ◽  
Asymptotic Variance ◽  
Regression Estimator ◽  
Variance Matrix ◽  
Percentile Method ◽  
Coverage Probabilities ◽  
Regression Estimators ◽  
Bootstrap Percentile ◽  
Bootstrap Distribution

The asymptotic variance matrix of the quantile regression estimator depends on the density of the error. For both deterministic and random regressors, the bootstrap distribution is shown to converge weakly to the limit distribution of the quantile regression estimator in probability. Thus, the confidence intervals constructed by the bootstrap percentile method have asymptotically correct coverage probabilities.

scholarly journals Weakly approaching sequences of random distributions

2000 ◽  
Vol 37 (3) ◽  
pp. 807-822 ◽  
Author(s):  
Yuri Belyaev ◽  
Sara Sjöstedt-de Luna
Keyword(s):  
Weak Convergence ◽  
Limit Distribution ◽  
Continuity Theorem ◽  
Statistics And Probability ◽  
Random Distributions

We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.

Aggressive Behavior and Problems of Self-Identity of Adolescents at 14–17 Years Old

2021 ◽  
pp. 49-56
Author(s):  
E. Pavlova
Keyword(s):  
Aggressive Behavior ◽  
Theory And Practice ◽  
Adolescent Psychology ◽  
Self Identity ◽  
Theoretical Literature ◽  
Identity Problems ◽  
Excessive Quantity

The problem of aggressive behavior of adolescents remains unresolved, and arouses great interest among psychologists, sociologists, criminologists. This is confirmed by a large number of articles and reports devoted to this problem, which appear annually in collections of scientific conferences. However, despite excessive quantity of theoretical literature devoted to adolescent psychology, there is a significant gap between theory and practice. The article attempts to move the problem of aggressive behavior of adolescents beyond individual external (social) and internal (characterological) factors to the global personological level and to consider it in the aspect of self-identity problems.

Imitation: Simple, Stretto, Canonical (On the Difficulties of Absolute Differentiation in the Polyphony of Strict Style)

2020 ◽  
pp. 26-39
Author(s):  
Т.В. Франтова
Keyword(s):  
20Th Century ◽  
18Th Century ◽  
Theory And Practice ◽  
Text Line ◽  
Theoretical Literature ◽  
The One ◽  
Different Sources ◽  
Stable Connection ◽  
Polyphonic Music ◽  
Musical Forms

Статья посвящена проблемам изучения теории и практики имитационной техники в полифонии строгого письма. Три типа имитации — простая, стреттная, каноническая — постоянно фигурируют в современной музыкально-теоретической литературе. Трактовки сути простой и канонической имитации в разных источниках совпадают, хотя формулировки в деталях разнятся. При этом значительны расхождения в понимании стретты. По традиции, заложенной учениями XVIII века, в теоретическом музыкознании стретту рассматривают в контексте формы фуги. Одновременно ряд исследователей считает возможным использовать понятие стретты по отношению к имитационному многоголосию Ренессанса. При этом термин употребляется в разных значениях. Материал исследования — начальные имитационные секции четырех-шестиголосных мотетов Палестрины без c. f. Тематическая организация рассматривается с учетом тексто-музыкальной формы мотета, в соответствии с которой функцию темы выполняет тексто-музыкальная строка, построенная на относительно стабильном соединении текстовой строки и развернутого мелодического soggetto. Ее неоднократные повторения позволяют обнаружить сходства и различия канонов и стретт в строгостильном многоголосии. The article is devoted to the problems of studying the theory and practice of imitation technique in polyphonic music of strict writing. Three types of imitation — simple, stretto and canonical — appear as relevant in modern musical theoretical literature. An analysis of the existing concepts showed that the interpretations of the essence of simple and canonical imitation in different sources coincide, although the formulations in details, as a rule, differ. Against this background, significant differences in the understanding of stretto (narrow, tight) imitation are especially noticeable. Many authors, foreign and domestic, starting from the teachings of the 18th century, consider the stretto in the context of the fugue form. At the same time, a number of researchers of the 20th century (domestic and foreign) have formed a different position. They believe that it is possible to expand the musical and historical boundaries of the use of the concept of stretto, its use in relation to the imitative polyphony of the Renaissance. The authors talk about the stretto in at least three different cases: the effect of a compressed temporary introduction of imitation voices (S. Skrebkov, T. Dubravskaya), narrow introduction of voices with their subsequent non-imitation promotion (N. Simakova), the tight entry of the rispost before the end of the theme in the propost, which does not fit into the canon (K. Eppessen, S. Skrebkov). The analysis of the musical material showed that the broadly understood stretto (the conciseness of the timing of the introduction of voices) is very typical of the polyphony of strict writing and manifests itself in many and different methods. The musical material of the study was the one-theme initial imitation sections of the four-six-part Palestrina motets, the compositional foundation of which lacks cantus firmus. The thematic organization was considered taking into account the genre of the motet, which belongs to the class of text-musical forms. In accordance with the nature of the genre, the function of the theme in the imitation section is performed by a text-musical line built on a relatively stable connection of a text line and an expanded melodic soggetto.

On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

1977 ◽  
Vol 14 (01) ◽  
pp. 114-126 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Gaussian Process ◽  
Point Process ◽  
Stationary Point ◽  
Stationary Gaussian Process ◽  
Time Curve ◽  
Second Moment ◽  
Stationary Point Process ◽  
Class Of Estimators

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ (V*(tTα ) – V(tTα )), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα ) is replaced by a suitable estimator.

The weak convergence of a class of estimators of the variance function of a two-dimensional Poisson process

1978 ◽  
Vol 15 (02) ◽  
pp. 433-439 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Poisson Process ◽  
Gaussian Process ◽  
Higher Dimensions ◽  
Variance Function ◽  
Stationary Gaussian Process ◽  
Two Dimensional ◽  
Second Moment ◽  
Class Of Estimators

Results of a previous paper (Liebetrau (1977a)) are extended to higher dimensions. An estimator V∗(t 1, t 2) of the variance function V(t 1, t 2) of a two-dimensional process is defined, and its first- and second-moment structure is given assuming the process to be Poisson. Members of a class of estimators of the form where and for 0 < α i < 1, are shown to converge weakly to a non-stationary Gaussian process. Similar results hold when the t′i are taken to be constants, when V is replaced by a suitable estimator and when the dimensionality of the underlying Poisson process is greater than two.

Approaches for dealing with various sources of overdispersion in modeling count data: Scale adjustment versus modeling

2015 ◽  
Vol 26 (4) ◽  
pp. 1802-1823 ◽  
Author(s):  
Elizabeth H Payne ◽  
James W Hardin ◽  
Leonard E Egede ◽  
Viswanathan Ramakrishnan ◽  
Anbesaw Selassie ◽  
...  
Keyword(s):  
Error Estimates ◽  
Standard Error ◽  
Count Data ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Rank Order ◽  
Good Practice ◽  
Information Criteria ◽  
Population Heterogeneity ◽  
Count Response

Overdispersion is a common problem in count data. It can occur due to extra population-heterogeneity, omission of key predictors, and outliers. Unless properly handled, this can lead to invalid inference. Our goal is to assess the differential performance of methods for dealing with overdispersion from several sources. We considered six different approaches: unadjusted Poisson regression (Poisson), deviance-scale-adjusted Poisson regression (DS-Poisson), Pearson-scale-adjusted Poisson regression (PS-Poisson), negative-binomial regression (NB), and two generalized linear mixed models (GLMM) with random intercept, log-link and Poisson (Poisson-GLMM) and negative-binomial (NB-GLMM) distributions. To rank order the preference of the models, we used Akaike's information criteria/Bayesian information criteria values, standard error, and 95% confidence-interval coverage of the parameter values. To compare these methods, we used simulated count data with overdispersion of different magnitude from three different sources. Mean of the count response was associated with three predictors. Data from two real-case studies are also analyzed. The simulation results showed that NB and NB-GLMM were preferred for dealing with overdispersion resulting from any of the sources we considered. Poisson and DS-Poisson often produced smaller standard-error estimates than expected, while PS-Poisson conversely produced larger standard-error estimates. Thus, it is good practice to compare several model options to determine the best method of modeling count data.

scholarly journals Developing Calibration Weights and Standard-Error Estimates for a Survey of Drug-Related Emergency-Department Visits

2014 ◽  
Vol 30 (3) ◽  
pp. 521-532 ◽  
Author(s):  
Phillip S. Kott ◽  
C. Daniel Day
Keyword(s):  
Emergency Department ◽  
Error Estimates ◽  
Standard Error ◽  
Emergency Department Visits ◽  
Simple Random Sample ◽  
Statistical Efficiency ◽  
Sampling Frame ◽  
Unit Nonresponse ◽  
Department Size ◽  
Hospital Emergency Departments

Abstract This article describes a two-step calibration-weighting scheme for a stratified simple random sample of hospital emergency departments. The first step adjusts for unit nonresponse. The second increases the statistical efficiency of most estimators of interest. Both use a measure of emergency-department size and other useful auxiliary variables contained in the sampling frame. Although many survey variables are roughly a linear function of the measure of size, response is better modeled as a function of the log of that measure. Consequently the log of size is a calibration variable in the nonresponse-adjustment step, while the measure of size itself is a calibration variable in the second calibration step. Nonlinear calibration procedures are employed in both steps. We show with 2010 DAWN data that estimating variances as if a one-step calibration weighting routine had been used when there were in fact two steps can, after appropriately adjusting the finite-population correct in some sense, produce standard-error estimates that tend to be slightly conservative.

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