scholarly journals Goodness of Fit Test of an Autocorrelated Time Series Cubic Smoothing Spline Model

2021 ◽  
pp. 191-200
Author(s):  
Samuel Olorunfemi Adams ◽  
Davies Abiodun Obaromi ◽  
Alumbugu Auta Irinews
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Real Life ◽  
Smoothing Spline ◽  
Selection Methods ◽  
Sample Sizes ◽  
Goodness Of Fit Test ◽  
Generalized Cross Validation ◽  
Non Parametric

We investigated the finite properties as well as the goodness of fit test for the cubic smoothing spline selection methods like the Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV) and Mallow CP criterion (MCP) estimators for time-series observation when there is the presence of Autocorrelation in the error term of the model. The Monte-Carlo study considered 1,000 replication with six sample sizes: 30; 60; 120; 240; 480 and 960, four degree of autocorrelations; 0.1; 0.3; 0.5; and 0.9 and three smoothing parameters; lambdaGML= 0.07271685, lambdaGCV= 0.005146929, lambdaMCP= 0.7095105. The cubic smoothing spline selection methods were also applied to a real-life dataset. The Predictive mean square error, R-square, and adjusted R-square criteria for assessing finite properties and goodness of fit among competing models discovered that the performance of the estimators is affected by changes in the sample sizes and autocorrelation levels of the simulated and real-life data set. The study concluded that the Generalized Cross-Validation estimator provides a better fit for Autocorrelated time series observation. It is recommended that the GCV works well at the four autocorrelation levels and provides the best fit for time-series observations at all sample sizes considered. This study can be applied to; non –parametric regression, non –parametric forecasting, spatial, survival and econometric observations.

On the use of chi-square analyses in studies of resource utilization

1991 ◽  
Vol 21 (1) ◽  
pp. 58-65 ◽  
Author(s):  
Dennis E. Jelinski
Keyword(s):  
Resource Utilization ◽  
Goodness Of Fit ◽  
Small Sample ◽  
Homogeneity Test ◽  
Type I ◽  
Sample Sizes ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Test Of Homogeneity ◽  
Small Sample Sizes

Chi-square (χ2) tests are analytic procedures that are often used to test the hypothesis that animals use a particular food item or habitat in proportion to its availability. Unfortunately, several sources of error are common to the use of χ2 analysis in studies of resource utilization. Both the goodness-of-fit and homogeneity tests have been incorrectly used interchangeably when resource availabilities are estimated or known apriori. An empirical comparison of the two methods demonstrates that the χ2 test of homogeneity may generate results contrary to the χ2 goodness-of-fit test. Failure to recognize the conservative nature of the χ2 homogeneity test, when "expected" values are known apriori, may lead to erroneous conclusions owing to the increased possibility of committing a type II error. Conversely, proper use of the goodness-of-fit method is predicated on the availability of accurate maps of resource abundance, or on estimates of resource availability based on very large sample sizes. Where resource availabilities have been estimated from small sample sizes, the use of the χ2 goodness-of-fit test may lead to type I errors beyond the nominal level of α. Both tests require adherence to specific critical assumptions that often have been violated, and accordingly, these assumptions are reviewed here. Alternatives to the Pearson χ2 statistic are also discussed.

scholarly journals A simple non-parametric goodness-of-fit test for elliptical copulas

2017 ◽  
Vol 5 (1) ◽  
pp. 330-353 ◽  
Author(s):  
Miriam Jaser ◽  
Stephan Haug ◽  
Aleksey Min
Keyword(s):  
Monte Carlo ◽  
Goodness Of Fit ◽  
Monte Carlo Study ◽  
Goodness Of Fit Test ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Nominal Level ◽  
Empirical Application ◽  
Non Parametric

AbstractIn this paper, we propose a simple non-parametric goodness-of-fit test for elliptical copulas of any dimension. It is based on the equality of Kendall’s tau and Blomqvist’s beta for all bivariate margins. Nominal level and power of the proposed test are investigated in a Monte Carlo study. An empirical application illustrates our goodness-of-fit test at work.

Adjusting a subject-specific time of event in longitudinal studies

2019 ◽  
Vol 29 (7) ◽  
pp. 1787-1798
Author(s):  
Hyunkeun Ryan Cho ◽  
Seonjin Kim ◽  
Myung Hee Lee
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Model Parameters ◽  
Specific Time ◽  
Goodness Of Fit Test ◽  
Proposed Model ◽  
Subject Specific ◽  
The Subject ◽  
The Mean ◽  
Over Time

Biomedical studies often involve an event that occurs to individuals at different times and has a significant influence on individual trajectories of response variables over time. We propose a statistical model to capture the mean trajectory alteration caused by not only the occurrence of the event but also the subject-specific time of the event. The proposed model provides a post-event mean trajectory smoothly connected with the pre-event mean trajectory by allowing the model parameters associated with the post-event mean trajectory to vary over time of the event. A goodness-of-fit test is considered to investigate how well the proposed model is fit to the data. Hypothesis tests are also developed to assess the influence of the subject-specific time of event on the mean trajectory. Theoretical and simulation studies confirm that the proposed tests choose the correctly specified model consistently and examine the effect of the subject-specific time of event successfully. The proposed model and tests are also illustrated by the analysis of two real-life data from a biomarker study for HIV patients along with their own time of treatment initiation and a body fatness study in girls with different age of menarche.

Analysis of Bridge Deflection Based on Time Series

2011 ◽  
Vol 71-78 ◽  
pp. 4545-4548 ◽  
Author(s):  
Lei Sun ◽  
Xian Wu Hao
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Goodness Of Fit ◽  
Arima Model ◽  
Least Square Method ◽  
Least Square ◽  
Monitoring Data ◽  
Goodness Of Fit Test ◽  
Bridge Monitoring ◽  
Series Analysis

The bridge health monitoring system can collect large amounts of data, but it lacks the trend analysis of monitoring data. This article introduced the method of Time series analysis into the analysis of bridge monitoring data, and adopted ARIMA model in time series analysis of monitoring data, used the least square method for parameter estimation, established the prediction model for bridge deflection, and conducted the goodness of fit test. Take the actual bridge monitoring data as an example, it was demonstrated that the method is feasible in the prediction of bridge condition trend.

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