scholarly journals Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments

2020 ◽  
Vol 24 ◽  
pp. 842-882
Author(s):  
Jean-Marc Azaïs ◽  
François Bachoc ◽  
Agnès Lagnoux ◽  
Thi Mong Ngoc Nguyen
Keyword(s):  
Gaussian Process ◽  
Scale Parameter ◽  
Parametric Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Mean And Variance ◽  
The Mean ◽  
The Moment ◽  
Quadratic Variations

We consider the semi-parametric estimation of the scale parameter of the variogram of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based both on quadratic variations and the moment method. We provide asymptotic approximations of the mean and variance of this estimator, together with asymptotic normality results, for a large class of Gaussian processes. We allow for general mean functions, provide minimax upper bounds and study the aggregation of several estimators based on various variation sequences. In extensive simulation studies, we show that the asymptotic results accurately depict the finite-sample situations already for small to moderate sample sizes. We also compare various variation sequences and highlight the efficiency of the aggregation procedure.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

Non-parametric estimation for a pure-jump Lévy process

2017 ◽  
Vol 12 (2) ◽  
pp. 338-349
Author(s):  
Chunhao Cai ◽  
Junyi Guo ◽  
Honglong You
Keyword(s):  
Risk Model ◽  
Low Frequency ◽  
Parametric Estimation ◽  
Large Sample Size ◽  
Simulation Studies ◽  
Finite Sample ◽  
Squared Error ◽  
The Laplace Transform ◽  
Integrated Squared Error ◽  
Non Parametric Estimation

AbstractIn this paper, we propose an estimator of the survival probability for a Lévy risk model observed at low frequency. The estimator is constructed via a regularised version of the inverse of the Laplace transform. The convergence rate of the estimator in a sense of the integrated squared error is studied for large sample size. Simulation studies are also given to show the finite sample performance of our estimator.

scholarly journals Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Farhad Yahgmaei ◽  
Manoochehr Babanezhad ◽  
Omid S. Moghadam
Keyword(s):  
Weibull Distribution ◽  
Scale Parameter ◽  
Loss Functions ◽  
Simulation Studies ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Risk Functions ◽  
Inverse Weibull Distribution ◽  
The Mean ◽  
Mean Square Errors

This paper proposes different methods of estimating the scale parameter in the inverse Weibull distribution (IWD). Specifically, the maximum likelihood estimator of the scale parameter in IWD is introduced. We then derived the Bayes estimators for the scale parameter in IWD by considering quasi, gamma, and uniform priors distributions under the square error, entropy, and precautionary loss functions. Finally, the different proposed estimators have been compared by the extensive simulation studies in corresponding the mean square errors and the evolution of risk functions.

scholarly journals Comparison of Some Semi-parametric Methods in Partial Linear Single-Index Model

2021 ◽  
Vol 27 (130) ◽  
pp. 170-184
Author(s):  
Huda Yahya Ahmed ◽  
Munaf Yousif Hmood
Keyword(s):  
Parametric Estimation ◽  
Estimation Methods ◽  
Model Estimation ◽  
Finite Sample ◽  
Two Stage ◽  
Single Index ◽  
Index Model ◽  
Single Index Model ◽  
The Mean ◽  
Partial Linear

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used

A DISCRETE QUEUE, FOURIER SAMPLING ON SZEGÖ CURVES AND SPITZER FORMULAS

2005 ◽  
Vol 03 (03) ◽  
pp. 361-387 ◽  
Author(s):  
A. J. E. M. JANSSEN ◽  
J. S. H. VAN LEEUWAARDEN
Keyword(s):  
Queue Length ◽  
Analytic Form ◽  
Moment Generating Function ◽  
Fourier Sampling ◽  
Stationary Queue Length ◽  
Server Queue ◽  
Mean And Variance ◽  
The Mean ◽  
The Moment ◽  
Multi Server

We consider a discrete-time multi-server queue for which the moments of the stationary queue length can be expressed in terms of series over the zeros in the closed unit disk of a queue-specific characteristic function. In many important cases these zeros can be considered to be located on a queue-specific curve, called generalized Szegö curve. By adopting a special parametrization of these Szegö curves, the relevant zeros occur as equidistant samples of a 2π-periodic function whose Fourier coefficients can be determined analytically. Thus the series occurring in the expressions for the moments can be written as Fourier aliasing series with terms given in analytic form. This gives rise to formulas for e.g. the mean and variance of the queue length that are reminiscent of Spitzer's identity for the moment generating function of the steady-state waiting time for a G/G/1 queue. Indeed, by considering the queue under investigation as a G/G/1 queue, the new formulas for the mean and variance also follow from Spitzer's identity. The approach in this paper can also be used to compute the probability distribution function of the queue length in analytic form.

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

scholarly journals Weighted statistical binary patterns for facial feature representation

2021 ◽  
Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim
Keyword(s):  
Comprehensive Evaluation ◽  
Facial Feature ◽  
Input Image ◽  
Feature Representation ◽  
Illumination Variation ◽  
Straight Line ◽  
Mean And Variance ◽  
The Mean ◽  
Face Datasets ◽  
Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

scholarly journals Groups and Individuals: Optical Flow Patterns of Broiler Chicken Flocks Are Correlated with the Behavior of Individual Birds

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 568
Author(s):  
Sabine G. Gebhardt-Henrich ◽  
Ariane Stratmann ◽  
Marian Stamp Dawkins
Keyword(s):  
Optical Flow ◽  
Broiler Chicken ◽  
Average Length ◽  
Flow Patterns ◽  
Group Level ◽  
Positive Correlation ◽  
Water Test ◽  
Mean And Variance ◽  
The Mean

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.

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