scholarly journals A note on confidence intervals for deblurred images

2020 ◽  
Vol 40 (3) ◽  
pp. 361-373
Author(s):  
Michał Biel ◽  
Zbigniew Szkutnik
Keyword(s):  
Inverse Problem ◽  
Confidence Intervals ◽  
Convolution Operator ◽  
Regression Models ◽  
Inverse Regression ◽  
Finite Sample ◽  
Bootstrap Confidence Intervals ◽  
Additive White Noise ◽  
Asymptotic Confidence Intervals ◽  
Simulation Results

We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.

Bootstrap pointwise confidence intervals for covariate-adjusted survivor functions in the Cox model

2019 ◽  
Vol 19 (1) ◽  
pp. 185-199
Author(s):  
Constantin Ruhe
Keyword(s):  
Confidence Intervals ◽  
Proportional Hazards ◽  
Cox Model ◽  
Survival Functions ◽  
Bootstrap Confidence Intervals ◽  
Cox Models ◽  
Varying Coefficients ◽  
Asymptotic Confidence Intervals ◽  
Time Varying Coefficients ◽  
Additional Option

Survival functions are a common visualization of predictions from the Cox model. However, neither Stata’s stcurve command nor the communitycontributed scurve tvc command allows one to estimate confidence intervals. In this article, I discuss how bootstrap confidence intervals can be formed for covariate-adjusted survival functions in the Cox model. The new bsurvci command automates this procedure and allows users to visualize the results. bsurvci enables one to estimate uncertainty around survival functions estimated from Cox models with time-varying coefficients, a capability that was not previously available in Stata. Furthermore, it provides Stata users with an additional option for survival estimates from Cox models with proportional hazards by allowing them to choose between bootstrap confidence intervals using bsurvci and asymptotic confidence intervals from an existing community-contributed command, survci. Because asymptotic confidence intervals make distributional assumptions when constructing confidence intervals, the bootstrap procedure proposed in this article provides a nonparametric alternative.

scholarly journals DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION

2010 ◽  
Vol 27 (3) ◽  
pp. 609-638 ◽  
Author(s):  
Stefan Hoderlein ◽  
Hajo Holzmann
Keyword(s):  
Inverse Problem ◽  
Nonparametric Regression ◽  
Regression Models ◽  
Unobserved Heterogeneity ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Problematic Relationship ◽  
Endogenous Regressors ◽  
Semiparametric Estimator ◽  
Ill Posed

In this paper we are concerned with analyzing the behavior of a semiparametric estimator that corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze its finite sample behavior. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages and the difficulties of an approach that leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between endogenous nonparametric regression models and the recently emphasized issue of unobserved heterogeneity in structural models.

Two-Condition Within-Participant Statistical Mediation Analysis: A Path-Analytic Framework

2019 ◽  
Author(s):  
Amanda Kay Montoya ◽  
Andrew F. Hayes
Keyword(s):  
Confidence Intervals ◽  
Indirect Effect ◽  
Mediation Analysis ◽  
Analytic Approach ◽  
Analytic Framework ◽  
Hypothesis Tests ◽  
Bootstrap Confidence Intervals ◽  
Complex Models ◽  
Path Analytic ◽  
Statistical Mediation Analysis

Researchers interested in testing mediation often use designs where participants are measured on a dependent variable Y and a mediator M in both of two different circumstances. The dominant approach to assessing mediation in such a design, proposed by Judd, Kenny, and McClelland (2001), relies on a series of hypothesis tests about components of the mediation model and is not based on an estimate of or formal inference about the indirect effect. In this paper we recast Judd et al.’s approach in the path-analytic framework that is now commonly used in between-participant mediation analysis. By so doing, it is apparent how to estimate the indirect effect of a within-participant manipulation on some outcome through a mediator as the product of paths of influence. This path analytic approach eliminates the need for discrete hypothesis tests about components of the model to support a claim of mediation, as Judd et al’s method requires, because it relies only on an inference about the product of paths— the indirect effect. We generalize methods of inference for the indirect effect widely used in between-participant designs to this within-participant version of mediation analysis, including bootstrap confidence intervals and Monte Carlo confidence intervals. Using this path analytic approach, we extend the method to models with multiple mediators operating in parallel and serially and discuss the comparison of indirect effects in these more complex models. We offer macros and code for SPSS, SAS, and Mplus that conduct these analyses.

A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

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