On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Petre Babilua ◽  
Elizbar Nadaraya
Keyword(s):  
Hypothesis Testing ◽  
Limiting Distribution ◽  
New Method ◽  
Testing Hypothesis ◽  
Test Power ◽  
Regression Functions

Abstract In the paper, the limiting distribution is established for an integral square deviation of estimates of Bernoulli regression functions based on two group samples. Based on these results, the new test is constructed for the hypothesis testing on the equality of two Bernoulli regression functions. The question of consistency of the constructed test is studied, and the asymptotic of the test power is investigated for some close alternatives.

Bayesian Based Multivariate Model Validation Method Under Uncertainty for Dynamic Systems

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Zhenfei Zhan ◽  
Yan Fu ◽  
Ren-Jye Yang ◽  
Yinghong Peng
Keyword(s):  
Data Analysis ◽  
Dynamic System ◽  
Hypothesis Testing ◽  
Uncertainty Quantification ◽  
Model Validation ◽  
Statistical Data ◽  
New Method ◽  
Statistical Data Analysis ◽  
Bayesian Hypothesis Testing ◽  
Repeated Test

Validation of computational models with multiple, repeated, and correlated functional responses for a dynamic system requires the consideration of uncertainty quantification and propagation, multivariate data correlation, and objective robust metrics. This paper presents a new method of model validation under uncertainty to address these critical issues. Three key technologies of this new method are uncertainty quantification and propagation using statistical data analysis, probabilistic principal component analysis (PPCA), and interval-based Bayesian hypothesis testing. Statistical data analysis is used to quantify the variabilities of the repeated tests and computer-aided engineering (CAE) model results. The differences between the mean values of test and CAE data are extracted as validation features, and the PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate difference curves. The variabilities of the repeated test and CAE data are propagated through the data transformation to the PPCA space. In addition, physics-based thresholds are defined and transformed to the PPCA space. Finally, interval-based Bayesian hypothesis testing is conducted on the reduced difference data to assess the model validity under uncertainty. A real-world dynamic system example which has one set of the repeated test data and two stochastic CAE models is used to demonstrate this new approach.

scholarly journals A New Method of Hypothesis Test for Truncated Spline Nonparametric Regression Influenced by Spatial Heterogeneity and Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Sifriyani ◽  
I. N. Budiantara ◽  
S. H. Kartiko ◽  
Gunardi
Keyword(s):  
Spatial Heterogeneity ◽  
Hypothesis Testing ◽  
Nonparametric Regression ◽  
Spatial Data ◽  
Hypothesis Test ◽  
Positive Semidefinite ◽  
New Method ◽  
Population Parameter ◽  
Test Statistic ◽  
Geographical Factor

This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H0 whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics V and verified that each of the numerators and denominators in the statistic test V followed a distribution of χ2. Since there was a symmetric and idempotent matrix S, it could be proved that Y~TS  Y~/σ2~χn-lm-12. Matrix Dui,vi was positive semidefinite and contained weighting matrix Wui,vi which had different values in every location; therefore matrix Dui,vi was not idempotent. If Y~TDui,viY~≥0 and Dui,vi was not idempotent and also Y~ was a N0,I distributed random vector, then there were constants k and r; hence Y~TDui,viY~~kχr2; therefore it was concluded that test statistic V followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia.

NONPARAMETRIC IDENTIFICATION AND ESTIMATION OF TRUNCATED REGRESSION MODELS WITH HETEROSKEDASTICITY

2017 ◽  
Vol 34 (3) ◽  
pp. 543-573
Author(s):  
Songnian Chen ◽  
Xun Lu ◽  
Xianbo Zhou ◽  
Yahong Zhou
Keyword(s):  
Regression Models ◽  
Regression Function ◽  
New Method ◽  
Nonparametric Identification ◽  
Conditional Heteroskedasticity ◽  
Truncated Regression ◽  
Finite Samples ◽  
Regression Functions ◽  
Economic Studies ◽  
Normally Distributed

We consider nonparametric identification and estimation of truncated regression models with unknown conditional heteroskedasticity. The existing methods (e.g., Chen (2010, Review of Economic Studies 77, 127–153)) that ignore heteroskedasticity often result in inconsistent estimators of regression functions. In this paper, we show that both the regression and heteroskedasticity functions are identified in a location-scale setting. Based on our constructive identification results, we propose kernel-based estimators of regression and heteroskedasticity functions and show that the estimators are asymptotically normally distributed. Our simulations demonstrate that our new method performs well in finite samples. In particular, we confirm that in the presence of heteroskedasticity, our new estimator of the regression function has a much smaller bias than Chen’s (2010, Review of Economic Studies 77, 127–153) estimator.

ANALISIS FAKTOR KEPERILAKUAN ORGANISASI TERHADAP KEGUNAAN SISTEM AKUNTANSI KEUANGAN DI BADAN KEUANGAN DAERAH PEMERINTAH PROVINSI SUMATERA BARAT

2017 ◽  
Vol 2 (3) ◽  
pp. 179
Author(s):  
Yulistia Yulistia ◽  
Novi Yanti ◽  
Ika Purwasih
Keyword(s):  
Hypothesis Testing ◽  
Hypothesis Test ◽  
Multiple Regression Model ◽  
Financial Accounting ◽  
Testing Hypothesis ◽  
Primary Data ◽  
Accounting System ◽  
Accounting Systems ◽  
Result Show ◽  
Dissemination Of Research

<p><em>This study aims to determine the effect of behavioral organization in the measure by training, clarity of purpose, and superior to the regional financial accounting system. Research sample is 30 respondent people have authority including civil servants who work in the financial sector in a body of regional financial the goverment province of West Sumatera . Data used are primary data obtained through questionare dissemination of research. In this research study variable grouped into two categories. The first independent variable consisted of the organization as measured by behavioral training, clarity of purpose and superior support. The second is the dependent variable is the area of financial accounting systems. To perform hypothesis testing is used in quantitative data analysis methods. Hypothesis test equipment used in the process of testing hypothesis is multiple regression model, statistical f-testand statistical t-test. Based on result of testing hypothesis was found that training did not significantly influence regional financial accounting system. The second hypothesis testing results show that the clarity of purpose did not significanlyt effect the usefulness of the area of  financial accounting system, the third hypothesis testing result indicate that support employer significant effect on the area of financial accounting system usability, while the fourth hypothesis testing result show that the training, clarity of purpose, and supervisor support a significant effect on the financial accounting system in a body of regional financial the goverment province of west sumatera.</em></p><p><span lang="EN-US">Penelitian ini bertujuan untuk mengetahui pengaruh keperilakuan organiasi yang diukur dengan pelatihan, kejelasan tujuan, dan dukungan atasan terhadap sistem akuntansi keuangan daerah. Penelitian dilakukan kepada 30 orang responden yang mempunyai wewenang dalam bidang keuangan di Badan Keuangan Daerah Pemerintah Provinsi Sumatera Barat. Data yang digunakan adalah data primer, yang diperoleh melalui penyebaran kuisioner penelitian. Di dalam penelitian ini dikelompokkan variabel penelitian ke dalam dua kategori. Pertama variabel independen yang terdiri dari keperilakuan organisasi yang diukur dengan pelatihan, kejelasan tujuan, dan dukungan atasan. Kedua adalah variabel dependen yaitu sistem akunatansi keuangan daerah. Untuk melakukan pengujian  hipotesis maka digunakan metode analisis data secara kuantitatif. Alat uji hipotesis yang digunakan dalam proses pengujian hipotesis adalah model regresi linear berganda, uji f-statistik dan uji t-statistik. Berdasarkan hasil pengujian hipotesis pertama ditemukan bahwa pelatihan tidak berpengaruh signifikan terhadap kegunaan sistem akuntansi keuangan daerah. Hasil pengujian hipotesis kedua menunjukkan bahwa kejelasan tujuan tidak berpengaruh signifikan terhadap kegunaan sistem akuntansi keuangan daerah. Hasil pengujian hipotesis ketiga menunjukkan bahwa dukungan atasan berpengaruh signifikan terhadap kegunaan sistem akuntansi keuangan daerah, sedangkan hasil pengujian hipotesis keempat menunjukkan bahwa pelatihan, kejelasan tujuan, dan dukungan atasan berpengaruh signifikan terhadap kegunaan sistem akuntansi keuangan di Badan Keuangan Daerah Pemerintah Provinsi Sumatera Barat.</span></p>

Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations

2018 ◽  
Vol 8 (1) ◽  
pp. 98-114 ◽  
Author(s):  
R. Lehmann ◽  
M. Lösler
Keyword(s):  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Statistical Test ◽  
Monte Carlo Integration ◽  
Ratio Test ◽  
Coordinate Transformations ◽  
Test Power ◽  
Non Linear ◽  
Decision Errors

Abstract In geodesy, hypothesis testing is applied to a wide area of applications e.g. outlier detection, deformation analysis or, more generally, model optimisation. Due to the possible far-reaching consequences of a decision, high statistical test power of such a hypothesis test is needed. The Neyman-Pearson lemma states that under strict assumptions the often-applied likelihood ratio test has highest statistical test power and may thus fulfill the requirement. The application, however, is made more difficult as most of the decision problems are non-linear and, thus, the probability density function of the parameters does not belong to the well-known set of statistical test distributions. Moreover, the statistical test power may change, if linear approximations of the likelihood ratio test are applied. The influence of the non-linearity on hypothesis testing is investigated and exemplified by the planar coordinate transformations. Whereas several mathematical equivalent expressions are conceivable to evaluate the rotation parameter of the transformation, the decisions and, thus, the probabilities of type 1 and 2 decision errors of the related hypothesis testing are unequal to each other. Based on Monte Carlo integration, the effective decision errors are estimated and used as a basis of valuation for linear and non-linear equivalents.

scholarly journals Polyhedral Star-Shaped Distributions

2017 ◽  
Vol 2017 ◽  
pp. 1-23 ◽  
Author(s):  
Wolf-Dieter Richter ◽  
Kay Schicker
Keyword(s):  
Hypothesis Testing ◽  
Generating Functions ◽  
New Method ◽  
Statistical Reasoning ◽  
Probabilistic Modelling ◽  
Real Dataset ◽  
Basic Properties ◽  
New Class ◽  
Moment Generating Functions ◽  
Scale Transformations

A new method of probabilistic modelling of polyhedrally contoured sample clouds is presented and applied to statistical reasoning for a real dataset. Various representations of the new class of polyhedral star-shaped distributions are derived and basic properties of the moments as well as characteristic and moment generating functions of these distributions are studied. Along with location-scale transformations, estimating and hypothesis testing are dealt with.

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