scholarly journals Kernel Estimation of Partial Means and a General Variance Estimator

1994 ◽  
Vol 10 (2) ◽  
pp. 1-21 ◽  
Author(s):  
Whitney K. Newey
Keyword(s):  
Asymptotic Normality ◽  
Consumer Surplus ◽  
Kernel Estimation ◽  
Delta Method ◽  
Regularity Conditions ◽  
Kernel Estimators ◽  
Variance Estimator ◽  
Method Variance ◽  
Nonparametric Models ◽  
Variance Estimates

Econometric applications of kernel estimators are proliferating, suggesting the need for convenient variance estimates and conditions for asymptotic normality. This paper develops a general “delta-method” variance estimator for functionals of kernel estimators. Also, regularity conditions for asymptotic normality are given, along with a guide to verify them for particular estimators. The general results are applied to partial means, which are averages of kernel estimators over some of their arguments with other arguments held fixed. Partial means have econometric applications, such as consumer surplus estimation, and are useful for estimation of additive nonparametric models.

scholarly journals Comparison of the Bootstrap and Delta Method Variances of the Variance Estimator of the Bernoulli Distribution

2018 ◽  
pp. 1-10
Author(s):  
Ying- Ying Zhang ◽  
Teng- Zhong Rong ◽  
Man- Man Li
Keyword(s):  
Bootstrap Method ◽  
Delta Method ◽  
Variance Estimator ◽  
Bernoulli Distribution ◽  
Bernoulli Trials ◽  
The Absolute ◽  
Variance Estimates ◽  
Parameter Values ◽  
The Bootstrap Method

It is interesting to calculate the variance of the variance estimator of the Bernoulli distribution. Therefore, we compare the Bootstrap and Delta Method variances of the variance estimator of the Bernoulli distribution in this paper. Firstly, we provide the correct Bootstrap, Delta Method, and true variances of the variance estimator of the Bernoulli distribution for three parameter values in Table 2.1. Secondly, we obtain the estimates of the variance of the variance estimator of the Bernoulli distribution by the Delta Method (analytically), the true method (analytically), and the Bootstrap Method (algorithmically). Thirdly, we compare the Bootstrap and Delta Methodsin terms of the variance estimates, the errors, and the absolute errors in three gures for 101 parameter values in [0, 1], with the purpose to explain the di erences between the Bootstrap and Delta Methods. Finally, we give three examples of the Bernoulli trials to illustrate the three methods.

ESTIMATING ADDITIVE NONPARAMETRIC MODELS BY PARTIAL Lq NORM: THE CURSE OF FRACTIONALITY

2001 ◽  
Vol 17 (6) ◽  
pp. 1037-1050
Author(s):  
Oliver Linton
Keyword(s):  
Asymptotic Normality ◽  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Regression Models ◽  
New Method ◽  
Kernel Estimators ◽  
One Dimensional ◽  
Nonparametric Models ◽  
Additive Nonparametric Regression ◽  
Consistency And Asymptotic Normality

We propose a new method for estimating additive nonparametric regression models based on taking the Lq median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q. For q > 3/2 one has the usual one-dimensional rate, but if q ≤ 3/2 the rate can be slower.

scholarly journals An approximate point-based alternative for the estimation of variance under big BAF sampling

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Thomas B. Lynch ◽  
Jeffrey H. Gove ◽  
Timothy G. Gregoire ◽  
Mark J. Ducey
Keyword(s):  
Forest Inventory ◽  
Variance Estimation ◽  
Basal Area ◽  
Volume Estimation ◽  
Delta Method ◽  
Sampling Point ◽  
Variance Estimator ◽  
Computer Simulation Studies ◽  
New Formula ◽  
Estimation Of Variance

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ 1 n where n is the number of sample points.

scholarly journals Universal inference

2020 ◽  
Vol 117 (29) ◽  
pp. 16880-16890 ◽  
Author(s):  
Larry Wasserman ◽  
Aaditya Ramdas ◽  
Sivaraman Balakrishnan
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Model Misspecification ◽  
Null Distribution ◽  
Regularity Conditions ◽  
Ratio Test ◽  
Finite Sample ◽  
Confidence Sets ◽  
Nonparametric Models

We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood-ratio statistic that we call “the split likelihood-ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood-ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum-likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid P values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes.

scholarly journals A Berry-Esseen Type Bound in Kernel Density Estimation for Negatively Associated Censored Data

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qunying Wu ◽  
Pingyan Chen
Keyword(s):  
Fixed Point ◽  
Censored Data ◽  
Kernel Estimation ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Regularity Conditions ◽  
Density Estimator ◽  
Negatively Associated ◽  
Kaplan Meier ◽  
Na Sequences

We discuss the kernel estimation of a density function based on censored data when the survival and the censoring times form the stationary negatively associated (NA) sequences. Under certain regularity conditions, the Berry-Esseen type bounds are derived for the kernel density estimator and the Kaplan-Meier kernel density estimator at a fixed pointx.

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