scholarly journals ASYMPTOTIC MEAN SQUARED ERROR OF KERNEL ESTIMATOR OF EXCESS DISTRIBUTION FUNCTION

2018 ◽  
Vol 50 ◽  
pp. 51-64
Author(s):  
Atsushi Shimokihara ◽  
Yoshihiko Maesono
Keyword(s):  
Distribution Function ◽  
Mean Squared Error ◽  
Kernel Estimator ◽  
Squared Error ◽  
Asymptotic Mean Squared Error

OPTIMAL BANDWIDTH CHOICE FOR ESTIMATION OF INVERSE CONDITIONAL–DENSITY–WEIGHTED EXPECTATIONS

2009 ◽  
Vol 26 (1) ◽  
pp. 94-118 ◽  
Author(s):  
David Tomás Jacho-Chávez
Keyword(s):  
Mean Squared Error ◽  
Kernel Estimator ◽  
Random Variable ◽  
Small Sample ◽  
Conditional Density ◽  
Monte Carlo Experiment ◽  
Continuous Random Variable ◽  
Optimal Bandwidth ◽  
Squared Error ◽  
Error Expansion

This paper characterizes the bandwidth value (h) that is optimal for estimating parameters of the form $\eta \, = \,E\left[ {\omega /f_{V|U} \left({V|U} \right)} \right]$, where the conditional density of a scalar continuous random variable V, given a random vector U, $f_{V|U} $, is replaced by its kernel estimator. That is, the parameter η is the expectation of ω inversely weighted by $f_{V|U} $, and it is the building block of various semiparametric estimators already proposed in the literature such as Lewbel (1998), Lewbel (2000b), Honoré and Lewbel (2002), Khan and Lewbel (2007), and Lewbel (2007). The optimal bandwidth is derived by minimizing the leading terms of a second-order mean squared error expansion of an in-probability approximation of the resulting estimator with respect to h. The expansion also demonstrates that the bandwidth can be chosen on the basis of bias alone, and that a simple “plug-in” estimator for the optimal bandwidth can be constructed. Finally, the small sample performance of our proposed estimator of the optimal bandwidth is assessed by a Monte Carlo experiment.

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.

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.

On the Autoregressive Model with Random Coefficients

1983 ◽  
Vol 32 (3-4) ◽  
pp. 135-142 ◽  
Author(s):  
D. Ray
Keyword(s):  
Autoregressive Model ◽  
Mean Squared Error ◽  
Second Order ◽  
Random Coefficients ◽  
Squared Error ◽  
Stationarity Conditions ◽  
Asymptotic Mean Squared Error

The first and second order stationarity conditions for an autore-gressive model with random coefficients are obtained. In addition, for such a type of model, the asymptotic mean squared error of an h-step ahead forecast is also considered.

scholarly journals Performance of Kernel Estimator and Johnson SB Function for Modeling Diameter Distribution of Black Alder (Alnus glutinosa (L.) Gaertn.) Stands

Forests ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 634 ◽  
Author(s):  
Piotr Pogoda ◽  
Wojciech Ochał ◽  
Stanisław Orzeł
Keyword(s):  
Mean Squared Error ◽  
Parametric Method ◽  
Kernel Estimator ◽  
Alnus Glutinosa ◽  
Diameter Distribution ◽  
Black Alder ◽  
Squared Error ◽  
Kolmogorov Smirnov ◽  
Test Sets ◽  
Anderson Darling

We compare the usefulness of nonparametric and parametric methods of diameter distribution modeling. The nonparametric method was represented by the new tool—kernel estimator of cumulative distribution function with bandwidths of 1 cm (KE1), 2 cm (KE2), and bandwidth obtained automatically (KEA). Johnson SB (JSB) function was used for the parametric method. The data set consisted of 7867 measurements made at breast height in 360 sample plots established in 36 managed black alder (Alnus glutinosa (L.) Gaertn.) stands located in southeastern Poland. The model performance was assessed using leave-one-plot-out cross-validation and goodness-of-fit measures: mean error, root mean squared error, Kolmogorov–Smirnov, and Anderson–Darling statistics. The model based on KE1 revealed a good fit to diameters forming training sets. A poor fit was observed for KEA. Frequency of diameters forming test sets were properly fitted by KEA and poorly by KE1. KEA develops more general models that can be used for the approximation of independent data sets. Models based on KE1 adequately fit local irregularities in diameter frequency, which may be considered as an advantageous in some situations and as a drawback in other conditions due to the risk of model overfitting. The application of the JSB function to training sets resulted in the worst fit among the developed models. The performance of the parametric method used to test sets varied depending on the criterion used. Similar to KEA, the JSB function gives more general models that emphasize the rough shape of the approximated distribution. Site type and stand age do not affect the fit of nonparametric models. The JSB function show slightly better fit in older stands. The differences between the average values of Kolmogorov–Smirnov (KS), Anderson–Darling (AD), and root mean squared error (RMSE) statistics calculated for models developed with test sets were statistically nonsignificant, which indicates the similar usefulness of the investigated methods for modeling diameter distribution.

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