scholarly journals SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES

2013 ◽  
Vol 30 (1) ◽  
pp. 176-200 ◽  
Author(s):  
Matias D. Cattaneo ◽  
Richard K. Crump ◽  
Michael Jansson
Keyword(s):  
Weighted Average ◽  
Standard Errors ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Small Bandwidth ◽  
Nominal Coverage ◽  
Error Formulas ◽  
Coverage Rates ◽  
Asymptotic Validity ◽  
Average Derivative

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (Econometrica 57, 1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels, and the standard errors are “robust” in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this papercoincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

scholarly journals Heteroskedasticity, temporal and spatial correlation matter

2013 ◽  
Vol 61 (7) ◽  
pp. 2151-2155
Author(s):  
Ladislava Grochová ◽  
Luboš Střelec
Keyword(s):  
Monte Carlo ◽  
Panel Data ◽  
Spatial Correlation ◽  
Serial Correlation ◽  
Asymptotic Theory ◽  
Standard Errors ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Cross Sectional ◽  
Cross Sectional Dimension

As economic time series or cross sectional data are typically affected by serial correlation and/or heteroskedasticity of unknown form, panel data typically contains some form of heteroskedasticity, serial correlation and/or spatial correlation. Therefore, robust inference in the presence of heteroskedasticity and spatial dependence is an important problem in spatial data analysis. In this paper we study the standard errors based on the HAC of cross-section averages that follows Vogelsang’s (2012) fixed-b asymptotic theory, i.e. we continue with Driscoll and Kraay approach (1998). The Monte Carlo simulations are used to investigate the finite sample properties of commonly used estimators both not accounting and accounting for heteroskedasticity and spatiotemporal dependence (OLS, GLS) in comparison to brand new estimator based on Vogelsang’s (2012) fixed-b asymptotic theory in the presence of cross-sectional heteroskedasticity and serial and spatial correlation in panel data with fixed effects. Our Monte Carlo experiment shows that the OLS exhibits an important downward bias in all of the cases and almost always has the worst performance when compared to the other estimators. The GLS corrected for HACSC performs well if time dimension is greater than cross-sectional dimension. The best performance can be attributed to the Vogelsang’s estimator with fixed-b version of Driscoll-Kraay standard errors.

scholarly journals AVERAGE DERIVATIVE ESTIMATION UNDER MEASUREMENT ERROR

2020 ◽  
pp. 1-30 ◽  
Author(s):  
Hao Dong ◽  
Taisuke Otsu ◽  
Luke Taylor
Keyword(s):  
Measurement Error ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Weighted Average ◽  
Error Characteristic ◽  
Finite Sample ◽  
Gaussian Density ◽  
Error Distributions ◽  
Error Density ◽  
Average Derivative

Abstract In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a particularly important class of error distribution as it includes the Gaussian density. We show that under either type of measurement error, despite using nonparametric deconvolution techniques and an estimated error characteristic function, we are able to achieve a $\sqrt {n}$ -rate of convergence for the average derivative estimator. Interestingly, if the measurement error density is symmetric, the asymptotic variance of the average derivative estimator is the same irrespective of whether the error density is estimated or not. The promising finite sample performance of the estimator is shown through a Monte Carlo simulation.

xtgeebcv: A command for bias-corrected sandwich variance estimation for GEE analyses of cluster randomized trials

2020 ◽  
Vol 20 (2) ◽  
pp. 363-381 ◽  
Author(s):  
John A. Gallis ◽  
Fan Li ◽  
Elizabeth L. Turner
Keyword(s):  
Randomized Trials ◽  
Variance Estimation ◽  
Public Health Education ◽  
Standard Errors ◽  
Future Research ◽  
Type I ◽  
Cluster Randomized Trials ◽  
Finite Sample ◽  
Individual Level ◽  
Cluster Randomized

Cluster randomized trials, where clusters (for example, schools or clinics) are randomized to comparison arms but measurements are taken on individuals, are commonly used to evaluate interventions in public health, education, and the social sciences. Analysis is often conducted on individual-level outcomes, and such analysis methods must consider that outcomes for members of the same cluster tend to be more similar than outcomes for members of other clusters. A popular individual-level analysis technique is generalized estimating equations (GEE). However, it is common to randomize a small number of clusters (for example, 30 or fewer), and in this case, the GEE standard errors obtained from the sandwich variance estimator will be biased, leading to inflated type I errors. Some bias-corrected standard errors have been proposed and studied to account for this finite-sample bias, but none has yet been implemented in Stata. In this article, we describe several popular bias corrections to the robust sandwich variance. We then introduce our newly created command, xtgeebcv, which will allow Stata users to easily apply finite-sample corrections to standard errors obtained from GEE models. We then provide examples to demonstrate the use of xtgeebcv. Finally, we discuss suggestions about which finite-sample corrections to use in which situations and consider areas of future research that may improve xtgeebcv.

ADMISSIBLE, SIMILAR TESTS: A CHARACTERIZATION

2019 ◽  
Vol 36 (2) ◽  
pp. 347-366 ◽  
Author(s):  
José Luis Montiel Olea
Keyword(s):  
Weight Function ◽  
Instrumental Variables ◽  
Structural Parameters ◽  
Average Power ◽  
Nuisance Parameter ◽  
Weighted Average ◽  
Necessary Condition ◽  
Ratio Test ◽  
Finite Sample ◽  
Characterization Result

This article studies a classical problem in statistical decision theory: a hypothesis test of a sharp null in the presence of a nuisance parameter. The main contribution of this article is a characterization of two finite-sample properties often deemed reasonable in this environment: admissibility and similarity. Admissibility means that a test cannot be improved uniformly over the parameter space. Similarity requires the null rejection probability to be unaffected by the nuisance parameter.The characterization result has two parts. The first part—established by Chernozhukov, Hansen, and Jansson (2009, Econometric Theory 25, 806–818)—states that maximizing weighted average power (WAP) subject to a similarity constraint suffices to generate admissible, similar tests. The second part—hereby established—states that constrained WAP maximization is (essentially) a necessary condition for a test to be admissible and similar. The characterization result shows that choosing an admissible, similar test is tantamount to selecting a particular weight function to report weighted average power. This result applies to full vector inference with a nuisance parameter, not to subvector inference.The article also revisits the theory of testing in the instrumental variables model. Specifically—and in light of the relevance of the weighted average power criterion in the main theoretical result—the article suggests a weight function for the structural parameters of the homoskedastic instrumental variables model, based on the priors proposed by Chamberlain (2007). The corresponding test is, by construction, admissible and similar. In addition, the test is shown to have finite- and large-sample properties comparable to those of the conditional likelihood ratio test.

Plant indicators of pH and water level in peatlands at Candle Lake, Saskatchewan

1971 ◽  
Vol 49 (9) ◽  
pp. 1661-1676 ◽  
Author(s):  
John K. Jeglum
Keyword(s):  
Water Level ◽  
Quantitative Data ◽  
Weighted Average ◽  
Similarity Coefficient ◽  
Standard Errors ◽  
Important Species ◽  
Environmental Correlates ◽  
Species Lists ◽  
Total Species ◽  
True Values

Quantitative data on vegetation, depth to water level, and pH of both moist peat and water from 113 stands of peatland near Candle Lake, Saskatchewan, are used to demonstrate relationships of peatland species to classes of pH and depth to water level, and to recognize plant indicators for the various classes. Weighted average and similarity coefficient techniques are used to estimate pH and depth to water level from total species lists and restricted lists of important species. Total species lists, combined with either weighted average or similarity coefficient techniques, yield indices with the highest correlations with the true values and the lowest standard errors of estimate. Depth to water level and pH are recognized as two important environmental correlates with floristic and vegetational variation in peatlands.

scholarly journals Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

2008 ◽  
Author(s):  
Matias D. Cattaneo ◽  
Richard K. Crump ◽  
Michael Jansson
Keyword(s):  
Weighted Average ◽  
Small Bandwidth

scholarly journals Efficiency of Weighted Average Derivative Estimators and Index Models

Econometrica ◽  
1993 ◽  
Vol 61 (5) ◽  
pp. 1199 ◽  
Author(s):  
Whitney K. Newey ◽  
Thomas M. Stoker
Keyword(s):  
Weighted Average ◽  
Average Derivative

scholarly journals Tropospheric moisture and its relation with rainfall due to nor’westers in Bangladesh

MAUSAM ◽  
2021 ◽  
Vol 58 (2) ◽  
pp. 153-160
Author(s):  
SAMARENDRA KARMAKAR ◽  
MD. MAHBUB ALAM
Keyword(s):  
Spatial Distribution ◽  
Water Content ◽  
Weighted Average ◽  
Precipitable Water ◽  
Specific Humidity ◽  
Standard Errors ◽  
Maximum Frequency ◽  
Maximum Rainfall ◽  
Average Water ◽  
Instability Indices

Attempts have been made to compute the precipitable water content of the troposphere, weighted average water vapour and to correlate these parameters with different instability indices and also with the next 24-hr rainfall, next 24-hr maximum rainfall and next 24-hr country averaged rainfall in order to predicting rainfall due to nor’westers in Bangladesh. It has been found that the maximum number of nor’westers occur when the precipitable water is 25-45 mm hr-1 between 1000 and 500 hPa, the maximum frequency being 48 in the range of 35-45 mm hr-1. The spatial distribution of precipitable water indicates that the maximum precipitable water is concentrated over the area near the places of nor’westers. The specific humidity has been found to increase on the dates of occurrence of nor’westers in Bangladesh on most occasions. Maximum number of nor’westers occurs when the weighted average specific humidity between the surface (1000 hPa) and 500 hPa is 8-12 g kg-1, the maximum frequency being 43 in the range of 8-10 g kg-1. The study reveals that nor’westers have been found to occur near or at the eastern end of maximum weighted average specific humidity. It has also been found that nor’westers occur near the point of inter-section of the axes of moist and dry zones. A number of parameters of the troposphere over Dhaka at 0000 UTC on the dates of occurrence of nor’westers such as precipitable water (mm/hr), MSWI, SWI, SWI/TT, (q1000 – q850) weighted averaged specific humidity have statistically significant correlations with next 24-hour rainfall at Dhaka, next 24-hour maximum rainfall in Bangladesh and country averaged rainfall. The correlation co-efficients are relatively small and the standard errors of estimates are higher. The small correlation co-efficients are significant because of the large number of data.

scholarly journals Nonparametric Instrumental-Variable Estimation

2018 ◽  
Vol 18 (4) ◽  
pp. 937-950 ◽  
Author(s):  
Denis Chetverikov ◽  
Dongwoo Kim ◽  
Daniel Wilhelm
Keyword(s):  
Instrumental Variable ◽  
Estimation Methods ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Gasoline Demand ◽  
Tuning Parameters ◽  
Demand Functions ◽  
Instrumental Variable Estimation ◽  
Finite Sample Properties ◽  
Shape Restriction

In this article, we introduce the commands npiv and npivcv, which implement nonparametric instrumental-variable (NPIV) estimation methods without and with a cross-validated choice of tuning parameters, respectively. Both commands can impose the constraint that the resulting estimated function is monotone. Using such a shape restriction may significantly improve the performance of the NPIV estimator (Chetverikov and Wilhelm, 2017, Econometrica 85: 1303–1320) because the ill-posedness of the NPIV estimation problem leads to unconstrained estimators that suffer from particularly poor statistical properties such as high variance. However, the constrained estimator that imposes the monotonicity significantly reduces variance by removing nonmonotone oscillations of the estimator. We provide a small Monte Carlo experiment to study the estimators’ finite-sample properties and an application to the estimation of gasoline demand functions.

scholarly journals TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

2019 ◽  
Vol 36 (4) ◽  
pp. 751-772 ◽  
Author(s):  
Javier Hualde ◽  
Morten Ørregaard Nielsen
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Relative Strength ◽  
Sum Of Squares ◽  
Monte Carlo Experiment ◽  
Time Series Models ◽  
Finite Sample ◽  
Generalized Polynomial ◽  
Finite Sample Properties ◽  
Deterministic Components

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

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