scholarly journals CONVERGENCE OF MSE OF A UNIFORM KERNEL ESTIMATOR FOR INTENSITY OF A PERIODIC POISSON PROCESS WITH UNKNOWN PERIOD

2009 ◽  
Vol 8 (2) ◽  
pp. 1
Author(s):  
I W. MANGKU
Keyword(s):  
Poisson Process ◽  
Mean Squared Error ◽  
Kernel Estimator ◽  
Joint Work ◽  
Squared Error ◽  
The One ◽  
Proof Of Convergence ◽  
Special Case ◽  
Unknown Period

Convergence of MSE (Mean-Squared-Error) of a uniform kernel estimator for intensity of a periodic Poisson process with unknowm period is presented and proved. The result presented here is a special case of the one in [3]. The aim of this paper is to present an alternative and a relatively simpler proof of convergence for the MSE of the estimator compared to the one in [3]. This is a joint work with R. Helmers and R. Zitikis.

scholarly journals STRONG CONVERGENCE OF A UNIFORM KERNEL ESTIMATOR FOR INTENSITY OF A PERIODIC POISSON PROCESS WITH UNKNOWN PERIOD

2009 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
I W. MANGKU
Keyword(s):  
Strong Convergence ◽  
Poisson Process ◽  
Kernel Estimator ◽  
Joint Work ◽  
The One ◽  
Special Case ◽  
Unknown Period

<p>Strong convergence of a uniform kernel estimator for intensity of a periodic Poisson process with unknowm period is presented and proved. The result presented here is a special case of the one in [3]. The aim of this paper is to present an alternative and a relatively simpler proof of strong convergence compared to the one in [3]. This is a joint work with R. Helmers and R. Zitikis.<br />1991 Mathematics Subject Classication: 60G55, 62G05, 62G20.</p>

scholarly journals CONSISTENCY OF A UNIFORM KERNEL ESTIMATOR FOR INTENSITY OF A PERIODIC POISSON PROCESS WITH UNKNOWN PERIOD

2008 ◽  
Vol 7 (2) ◽  
pp. 31
Author(s):  
I W. MANGKU
Keyword(s):  
Poisson Process ◽  
Kernel Estimator ◽  
Joint Work ◽  
Classi Cation ◽  
Special Case ◽  
Unknown Period

<p>A uniform kernel estimator for intensity of a periodic Poisson process with unknowm period is presented and a proof of its consistency is discussed. The result presented in this paper is a special case of that in [3]. The aim of discussing a uniform kernel estimator is in order to be able to present a relatively simpler proof of consistency compared to that in [3]. This is a joint work with R. Helmers and R. Zitikis.<br />1991 Mathematics Subject Classi¯cation: 60G55, 62G05, 62G20.</p>

Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable

1993 ◽  
Vol 9 (1) ◽  
pp. 62-80 ◽  
Author(s):  
Jan F. Kiviet ◽  
Garry D.A. Phillips
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Small Sample ◽  
Large Sample ◽  
Squared Error ◽  
Coefficient Vector ◽  
Lagged Dependent Variable ◽  
Biased Estimators ◽  
The One

The small sample bias of the least-squares coefficient estimator is examined in the dynamic multiple linear regression model with normally distributed whitenoise disturbances and an arbitrary number of regressors which are all exogenous except for the one-period lagged-dependent variable. We employ large sample (T → ∞) and small disturbance (σ → 0) asymptotic theory and derive and compare expressions to O(T−1) and to O(σ2), respectively, for the bias in the least-squares coefficient vector. In some simulations and for an empirical example, we examine the mean (squared) error of these expressions and of corrected estimation procedures that yield estimates that are unbiased to O(T−l) and to O(σ2), respectively. The large sample approach proves to be superior, easily applicable, and capable of generating more efficient and less biased estimators.

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 $\eta \, &#x003D; \,E\left[ {\omega /f_{V|U} \left({V|U} \right)} \right]$, 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.

Comparison of some annual forest inventory estimators

2002 ◽  
Vol 32 (11) ◽  
pp. 1992-1995 ◽  
Author(s):  
Paul C Van Deusen
Keyword(s):  
Forest Inventory ◽  
Mean Squared Error ◽  
Moving Average ◽  
Current Status ◽  
Quadratic Growth ◽  
Growth Trends ◽  
Squared Error ◽  
Mixed Estimator ◽  
The One ◽  
Panel Design

Three estimators of current status and trend are compared for an annual interpenetrating panel design. The five-panel annual inventory design is simulated over a 10-year period with flat, increasing, and quadratic growth trends. The simulated comparisons show that the mixed estimator performs well relative to the 5-year moving average in terms of bias and mean squared error in all cases. The one-panel mean can have less bias than the moving average when there is a trend, but it is more variable. The moving average tends to lag evolving trends, which can result in very large bias.

Inference for stationary random fields given Poisson samples

1986 ◽  
Vol 18 (2) ◽  
pp. 406-422 ◽  
Author(s):  
Alan F. Karr
Keyword(s):  
Random Field ◽  
Poisson Process ◽  
Random Fields ◽  
Covariance Function ◽  
Mean Squared Error ◽  
Compact Sets ◽  
Mild Conditions ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
The Mean

Given a d-dimensional random field and a Poisson process independent of it, suppose that it is possible to observe only the location of each point of the Poisson process and the value of the random field at that (randomly located) point. Non-parametric estimators of the mean and covariance function of the random field—based on observation over compact sets of single realizations of the Poisson samples—are constructed. Under fairly mild conditions these estimators are consistent (in various senses) as the set of observation becomes unbounded in a suitable manner. The state estimation problem of minimum mean-squared error reconstruction of unobserved values of the random field is also examined.

scholarly journals A new family of polyno-expo-trigonometric distributions with applications

2019 ◽  
Vol 22 (04) ◽  
pp. 1950027
Author(s):  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Mean Squared Error ◽  
Real Life ◽  
Likelihood Method ◽  
Lifetime Data ◽  
New Family ◽  
Squared Error ◽  
The Mean ◽  
Special Case

In this paper, a new family of polyno-expo-trigonometric distributions is presented and investigated. A special case using the Weibull distribution, with three parameters, is considered as statistical model for lifetime data. The estimation of the parameters is performed with the maximum likelihood method. A numerical simulation study verifies that the bias and the mean squared error of the maximum likelihood estimators tend to zero as the sample size is increased. Three real life datasets are then analyzed. We show that our model has a good fit in comparison to the other well-known powerful models in the literature.

scholarly journals Ascertaining Time Series Predictability in Process Control – Case Study on Rainfall Prediction

2018 ◽  
Vol 203 ◽  
pp. 07002
Author(s):  
Chandrasekaran Sivapragasam ◽  
Poomalai Saravanan ◽  
Saminathan Balamurali ◽  
Nitin Muttil
Keyword(s):  
Time Series ◽  
Process Control ◽  
Hurst Exponent ◽  
Mean Squared Error ◽  
Rain Gauge ◽  
Natural Phenomenon ◽  
Rainfall Prediction ◽  
Squared Error ◽  
The One

Rainfall prediction is a challenging task due to its dependency on many natural phenomenon. Some authors used Hurst exponent as a predictability indicator to ensure predictability of the time series before prediction. In this paper, a detailed analysis has been done to ascertain whether a definite relation exists between a strong Hurst exponent and predictability. The one-lead monthly rainfall prediction has been done for 19 rain gauge station of the Yarra river basin in Victoria, Australia using Artificial Neural Network. The prediction error in terms of normalized Root Mean Squared Error has been compared with Hurst exponent. The study establishes the truth of the hypothesis for only 6 stations out of 19 stations, and thus recommends further investigation to prove the hypothesis. This concept is relevant for any time series which need to be used for real time process control.

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.

scholarly journals Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Martin M. Kithinji ◽  
Peter N. Mwita ◽  
Ananda O. Kube
Keyword(s):  
Value At Risk ◽  
Mean Squared Error ◽  
Conditional Value At Risk ◽  
Conditional Quantile ◽  
Squared Error ◽  
Quantile Autoregression ◽  
Simulation Results ◽  
The One ◽  
Conditional Quantile Estimator ◽  
Extreme Conditional Quantile

In this paper, we propose an extreme conditional quantile estimator. Derivation of the estimator is based on extreme quantile autoregression. A noncrossing restriction is added during estimation to avert possible quantile crossing. Consistency of the estimator is derived, and simulation results to support its validity are also presented. Using Average Root Mean Squared Error (ARMSE), we compare the performance of our estimator with the performances of two existing extreme conditional quantile estimators. Backtest results of the one-day-ahead conditional Value at Risk forecasts are also given.

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