Rates of Expansions for Functional Estimators

2021 ◽  
Author(s):  
Yulia Kotlyarova ◽  
Marcia M. A. Schafgans ◽  
Victoria Zinde-Walsh
Keyword(s):  
Convergence Rates ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Finite Sample ◽  
Squared Error ◽  
Semiparametric Estimators ◽  
Asymptotic Mean Squared Error ◽  
The Impact ◽  
Nonconvex Model

AbstractIn this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness.

scholarly journals Optimal designs for frequentist model averaging

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 665-682
Author(s):  
K Alhorn ◽  
K Schorning ◽  
H Dette
Keyword(s):  
Mean Squared Error ◽  
Model Averaging ◽  
Optimal Solution ◽  
Regression Function ◽  
Optimal Designs ◽  
Squared Error ◽  
Bayesian Optimal Design ◽  
The Mean ◽  
Asymptotic Mean Squared Error ◽  
Frequentist Model Averaging

SummaryWe consider the problem of designing experiments for estimating a target parameter in regression analysis when there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed that chooses the experimental design to minimize the asymptotic mean squared error of the frequentist model averaging estimate. Necessary conditions for the optimal solution of a locally and Bayesian optimal design problem are established. The results are illustrated in several examples, and it is demonstrated that Bayesian optimal designs can yield a reduction of the mean squared error of the model averaging estimator by up to 45%.

Generalized Forecast Averaging in Autoregressions with a Near Unit Root

2020 ◽  
Author(s):  
Mohitosh Kejriwal ◽  
Xuewen Yu
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Finite Sample ◽  
Deterministic Components ◽  
Asymptotic Mean Squared Error ◽  
Near Unit Root

Summary This paper develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. Within a local-to-unity asymptotic framework, we derive analytical expressions for the asymptotic mean squared error and one-step-ahead mean squared forecast risk of the proposed estimator and show that the optimal FGLS weights are different from their ordinary least squares (OLS) counterparts. We also provide theoretical justification for a generalized Mallows averaging estimator that incorporates lag order uncertainty in the construction of the forecast. Monte Carlo simulations demonstrate that the proposed procedure yields a considerably lower finite-sample forecast risk relative to OLS averaging. An application to U.S. macroeconomic time series illustrates the efficacy of the advocated method in practice and finds that both persistence and lag order uncertainty have important implications for the accuracy of forecasts.

scholarly journals Automated Bale Mapping Using Machine Learning and Photogrammetry

2021 ◽  
Vol 13 (22) ◽  
pp. 4675
Author(s):  
William Yamada ◽  
Wei Zhao ◽  
Matthew Digman
Keyword(s):  
Lower Cost ◽  
Mean Squared Error ◽  
Spatial Clustering ◽  
Mean Average Precision ◽  
Average Precision ◽  
Data Set ◽  
Map Projection ◽  
Squared Error ◽  
Aerial Vehicle ◽  
The Impact

An automatic method of obtaining geographic coordinates of bales using monovision un-crewed aerial vehicle imagery was developed utilizing a data set of 300 images with a 20-megapixel resolution containing a total of 783 labeled bales of corn stover and soybean stubble. The relative performance of image processing with Otsu’s segmentation, you only look once version three (YOLOv3), and region-based convolutional neural networks was assessed. As a result, the best option in terms of accuracy and speed was determined to be YOLOv3, with 80% precision, 99% recall, 89% F1 score, 97% mean average precision, and a 0.38 s inference time. Next, the impact of using lower-cost cameras was evaluated by reducing image quality to one megapixel. The lower-resolution images resulted in decreased performance, with 79% precision, 97% recall, 88% F1 score, 96% mean average precision, and 0.40 s inference time. Finally, the output of the YOLOv3 trained model, density-based spatial clustering, photogrammetry, and map projection were utilized to predict the geocoordinates of the bales with a root mean squared error of 2.41 m.

scholarly journals Effect of unfavourable population structure on estimates of heritability, systematic effects and breeding values

2008 ◽  
Vol 51 (6) ◽  
pp. 601-610
Author(s):  
A. P. Kominakis
Keyword(s):  
Population Structure ◽  
Mean Squared Error ◽  
Heritability Estimate ◽  
Breeding Values ◽  
Parameter Estimations ◽  
Squared Error ◽  
Heritability Estimation ◽  
Population Structures ◽  
Systematic Effects ◽  
The Impact

Abstract. Empirical estimations of heritability, systematic effects and predictions of sires’ breeding values (BVs) were obtained under various population structures for simulated populations consisted of n = 400 animals in 5 herds for a trait of medium heritability (h2 = 0.30). An infinitesimal additive genetic animal model was assumed while simulating data. Population structure was varied to allow for good and poor connectedness across herds and (non)random association between the genetic and the environmental effects. The impact of the various population structures on the parameter estimation(s) was assessed using Mean Squared Error (MSE) and Pearson’s correlations. Allowing sires to have progenies in more than one herd (good herd connectedness) and random use of sires across herds generally resulted in good parameter estimations. Poor connectedness significantly affected herd effects estimation and BV prediction but not heritability estimation as long as random usage of sires across environments was guaranteed. Selective use of the best sires in the best herds along with poor connectedness resulted in poorest estimations of all parameters examined. In the latter case, heritability was seriously underestimated (h2 = 0.06) while highest error, lowest accuracies for the BVs and a remarkable underestimation of the genetic gain were observed. Use of reference sires on a natural mating basis to create genetic links between herds has served a good solution for both heritability and BVs estimation under unfavorable structure. Mating 0.25 of the herd ewes with reference sires resulted in a heritability estimate close to the simulated one. Significantly better estimates of systematic effects and BVs were, however, obtained when 0.5 of the herd ewes were mated by reference sires.

FINITE-SAMPLE MOMENTS OF THE COEFFICIENT OF VARIATION

2009 ◽  
Vol 25 (1) ◽  
pp. 291-297 ◽  
Author(s):  
Yong Bao
Keyword(s):  
Coefficient Of Variation ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
General Distribution ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Finite Sample Bias ◽  
Sample Coefficient Of Variation

We study the finite-sample bias and mean squared error, when properly defined, of the sample coefficient of variation under a general distribution. We employ a Nagar-type expansion and use moments of quadratic forms to derive the results. We find that the approximate bias depends on not only the skewness but also the kurtosis of the distribution, whereas the approximate mean squared error depends on the cumulants up to order 6.

scholarly journals Dynamic Regression and Filtered Data Series: A Laplace Approximation to the Effects of Filtering in Small Samples

1996 ◽  
Vol 12 (3) ◽  
pp. 432-457 ◽  
Author(s):  
Eric Ghysels ◽  
Offer Lieberman
Keyword(s):  
Regression Model ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
Small Sample ◽  
Data Series ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Lagged Dependent Variable ◽  
Dynamic Regression Model

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample bias and mean squared error. In general, these results entail a numerical integration of derivatives of the joint moment generating function of two quadratic forms in normal variables. The computation of these integrals is quite involved. However, we take advantage of the Laplace approximations to the bias and mean squared error, which substantially reduce the computational burden, as they yield relatively simple analytic expressions. We obtain analytic formulae for approximating the effect of filtering on the finite sample bias and mean squared error. We evaluate the adequacy of the approximations by comparison with Monte Carlo simulations, using the Census X-11 filter as a specific example

Finite Sample Properties of Several Predictors From an Autoregressive Model

1987 ◽  
Vol 3 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Koichi Maekawa
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Asymptotic Expansions ◽  
Autoregressive Model ◽  
Mean Squared Error ◽  
The Other ◽  
Finite Sample ◽  
Squared Error ◽  
Distributional Properties ◽  
Finite Sample Properties

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O(T−1), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to O(T−1).

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

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