On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity

1994 ◽  
Vol 10 (1) ◽  
pp. 70-90 ◽  
Author(s):  
R.M. de Jong ◽  
H.J. Bierens
Keyword(s):  
Infinite Number ◽  
Fixed Number ◽  
Model Specification ◽  
Test Statistic ◽  
Conditional Moment ◽  
Chi Square ◽  
Moment Conditions ◽  
Conditional Moments ◽  
Finite Samples ◽  
Consistent Model

In this paper, a consistent model specification test is proposed. Some consistent model specification tests have been discussed in econometrics literature. Those tests are consistent by randomization, display a discontinuity in sample size, or have an asymptotic distribution that depends on the data-generating process and on the model, whereas our test does not have one of those disadvantages. Our test can be viewed upon as a conditional moment test as proposed by Newey but instead of a fixed number of conditional moments, an asymptotically infinite number of moment conditions is employed. The use of an asymptotically infinite number of conditional moments will make it possible to obtain a consistent test. Computation of the test statistic is particularly simple, since in finite samples our statistic is equivalent to a chi-square conditional moment test of a finite number of conditional moments.

scholarly journals Testing a Parametric Model Against a Semiparametric Alternative

1994 ◽  
Vol 10 (5) ◽  
pp. 821-848 ◽  
Author(s):  
Joel L. Horowitz ◽  
Wolfgang Härdle
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Random Variable ◽  
Parametric Model ◽  
Conditional Moment ◽  
Moment Conditions ◽  
Explanatory Variables ◽  
Conditional Moments ◽  
Monte Carlo Experiments ◽  
The Mean

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.

scholarly journals A FLEXIBLE NONPARAMETRIC TEST FOR CONDITIONAL INDEPENDENCE

2015 ◽  
Vol 32 (6) ◽  
pp. 1434-1482 ◽  
Author(s):  
Meng Huang ◽  
Yixiao Sun ◽  
Halbert White
Keyword(s):  
Conditional Independence ◽  
Kernel Smoothing ◽  
Nonparametric Test ◽  
Nuisance Parameters ◽  
Local Power ◽  
Test Statistic ◽  
Conditional Moment ◽  
Finite Samples ◽  
Monte Carlo Experiments ◽  
Logistic Functions

This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n−1/2 local power. The test statistic is based on an estimator of the topological “distance” between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in finite samples. As an application, we test an implication of the key assumption of unconfoundedness in the context of estimating the returns to schooling.

CONSISTENT MODEL SPECIFICATION TESTS

2000 ◽  
Vol 16 (6) ◽  
pp. 1016-1041 ◽  
Author(s):  
Yanqin Fan ◽  
Qi Li
Keyword(s):  
Nonparametric Tests ◽  
Model Specification ◽  
Local Alternatives ◽  
Exponential Weight ◽  
Conditional Moment ◽  
Specification Tests ◽  
Consistent Model ◽  
Close Relationship ◽  
Complex Valued ◽  
Theoretical Results

We point out the close relationship between the integrated conditional moment tests in Bierens (1982, Journal of Econometrics 20, 105–134) and Bierens and Ploberger (1997, Econometrica 65, 1129–1152) with the complex-valued exponential weight function and the kernel-based tests in Härdle and Mammen (1993, Annals of Statistics 21, 1926–1947), Li and Wang (1998, Journal of Econometrics 87, 145–165), and Zheng (1996, Journal of Econometrics 75, 263–289). It is well established that the integrated conditional moment tests of Bierens (1982) and Bierens and Ploberger (1997) are more powerful than kernel-based nonparametric tests against Pitman local alternatives. In this paper we analyze the power properties of the kernel-based tests and the integrated conditional moment tests for a sequence of “singular” local alternatives, and show that the kernel-based tests can be more powerful than the integrated conditional moment tests for these “singular” local alternatives. These results suggest that integrated conditional moment tests and kernel-based tests should be viewed as complements to each other. Results from a simulation study are in agreement with the theoretical results.

scholarly journals WEAK-IDENTIFICATION ROBUST WILD BOOTSTRAP APPLIED TO A CONSISTENT MODEL SPECIFICATION TEST

2020 ◽  
pp. 1-55
Author(s):  
Jonathan B. Hill
Keyword(s):  
Bootstrap Method ◽  
Nuisance Parameter ◽  
Covariance Structure ◽  
Model Specification ◽  
Wild Bootstrap ◽  
Test Statistic ◽  
Conditional Moment ◽  
Uniform Size ◽  
Weak Identification ◽  
Empirical Size

We present a new robust bootstrap method for a test when there is a nuisance parameter under the alternative, and some parameters are possibly weakly or nonidentified. We focus on a Bierens (1990, Econometrica 58, 1443–1458)-type conditional moment test of omitted nonlinearity for convenience. Existing methods include the supremum p-value which promotes a conservative test that is generally not consistent, and test statistic transforms like the supremum and average for which bootstrap methods are not valid under weak identification. We propose a new wild bootstrap method for p-value computation by targeting specific identification cases. We then combine bootstrapped p-values across polar identification cases to form an asymptotically valid p-value approximation that is robust to any identification case. Our wild bootstrap procedure does not require knowledge of the covariance structure of the bootstrapped processes, whereas Andrews and Cheng’s (2012a, Econometrica 80, 2153–2211; 2013, Journal of Econometrics 173, 36–56; 2014, Econometric Theory 30, 287–333) simulation approach generally does. Our method allows for robust bootstrap critical value computation as well. Our bootstrap method (like conventional ones) does not lead to a consistent p-value approximation for test statistic functions like the supremum and average. Therefore, we smooth over the robust bootstrapped p-value as the basis for several tests which achieve the correct asymptotic level, and are consistent, for any degree of identification. They also achieve uniform size control. A simulation study reveals possibly large empirical size distortions in nonrobust tests when weak or nonidentification arises. One of our smoothed p-value tests, however, dominates all other tests by delivering accurate empirical size and comparatively high power.

On the Use of Artificial Regressions in Certain Microeconometric Models

1995 ◽  
Vol 11 (2) ◽  
pp. 290-305 ◽  
Author(s):  
Chris Orme
Keyword(s):  
Null Model ◽  
Model Specification ◽  
Finite Sample ◽  
Test Statistic ◽  
Parameter Estimator ◽  
Conditional Moment ◽  
Outer Product ◽  
Conditional Statistics

Conditional moment tests check to see whether or not population moment equalities, implied by the null model specification, hold approximately in the sample. Asymptotically valid conditional statistics can easily be calculated from the output of a so-called outer product of the gradient (OPG) artificial regression. However, several studies have now found that this OPG variant exhibits extremely poor finite sample behavior and that significant improvements can be made by employing the efficient variant. In the light of such evidence, this paper develops new artificial regressions that can be used to calculate the efficient variant of the test statistic. These artificial regressions can also serve several other purposes, including the construction of Hausmantype tests of parameter estimator consistency.

The Hausman Test Statistic can be Negative even Asymptotically

2008 ◽  
Vol 228 (4) ◽  
Author(s):  
Sven Schreiber
Keyword(s):  
Alternative Hypothesis ◽  
Nuisance Parameter ◽  
Null Distribution ◽  
Formal Proof ◽  
Small Samples ◽  
Homogeneity Test ◽  
Residual Variance ◽  
Test Statistic ◽  
Chi Square ◽  
Finite Samples

SummaryWe show that under the alternative hypothesis the Hausman chi-square test statistic can be negative not only in small samples but even asymptotically. Therefore in large samples such a result is only compatible with the alternative and should be interpreted accordingly. Applying a known insight from finite samples, this can only occur if the different estimation precisions (often the residual variance estimates) under the null and the alternative both enter the test statistic. In finite samples, using the absolute value of the test statistic is a remedy that does not alter the null distribution and is thus admissible. Even for positive test statistics the relevant covariance matrix difference should be routinely checked for positive semi-definiteness, because we also show that otherwise test results may be misleading. Of course the preferable solution still is to impose the same nuisance parameter (i.e., residual variance) estimate under the null and alternative hypotheses, if the model context permits that with relative ease. We complement the likelihood-based exposition by a formal proof in an omitted-variable context, we present simulation evidence for the test of panel random effects, and we illustrate the problems with a panel homogeneity test.

HUBUNGAN ANTARA UMUR DAN PENDIDIKAN IBU DENGAN KEJADIAN BBLR DI RUMAH SAKIT UMUM PUSAT DR. MOHAMMAD HOESIN PALEMBANG TAHUN 2010

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Yuhemy Zurizah Yuhemy Zurizah ◽  
Rini Mayasari Rini Mayasari
Keyword(s):  
General Hospital ◽  
Maternal Age ◽  
Public Hospitals ◽  
Infant Mortality Rate ◽  
P Value ◽  
Check List ◽  
Test Statistic ◽  
Chi Square ◽  
Cross Sectional ◽  
Live Births

ABSTRACT Low Birth Weight (LBW) was defined as infants born weighing less than 2.500 grams. WHO estimates that nearly all (98%) of the five million neonatal deaths in developing countries. According to City Health if Palembang Departement, infant mortality rate (IMR) in the year 2007 is 3 per 1000 live births, in 2008 four per 1000 live births, and in 2009 approximately 2 per 1000 live births. The cause of LBW is a disease, maternal age, social circumstances, maternal habits factors, fetal factors and environmental factors. LBW prognosis depending on the severity of the perinatal period such as stage of gestation (gestation getting younger or lower the baby's weight, the higher the mortality), asphyxia / ischemia brain, respiratory distress syndromesmetabolic disturbances. This study aims to determine the relationship between maternal age and educations mothers of pregnancy with the incidence of LBW in the General Hospital Dr Center. Mohammad Hoesin Palembang in 2010 This study uses the Analytical Ceoss Sectional Survey. The study population was all mothers who gave birth in public hospitals center Dr. Mohammad Hoesin Palembang in 2010 were 1.476 mothers gave birth with a large sample of 94 studies of maternal taken by systematic random sampling, ie research instument Check List. Data analysis was performed univariate and bivariate. The results of this study show from 94 mothers of LBW was found 45 people (47,9%) Which has a high risk age 26 LBW ( 27,7%) while the distance of low educations LBW (55,3%). From Chi-Square test statistic that compares the p value with significance level α = 0,05 showed a significant correlation between maternal age, where the p value = 0,002, of education mothers of pregnancy p value = 0,003 with LBW. In the general hospital center Dr. Mohammad Hoesin Palembang ini 2010. Expected to researches who will come to examine in more depth.   ABSTRAK Bayi Berat Lahir Rendah (BBLR) telah didefinisikan sebagai bayi lahir kurang dari 2.500 gram. WHO memperkirakan hampir semua (98%) dari 5 juta kematian neonatal di negara berkembang. Menurut Data Dinas Kesehatan Kota Palembang, Angka Kematian Bayi (AKB) pada tahun 2007 yaitu 3 per 1.000 kelahiran hidup, pada tahun 2008 4 per 1.000 kelahiran hidup, dan pada tahun 2009 sekitar 2 per 1.000 kelahiran hidup. Penyebab BBLR adalah penyakit, usia ibu, keadaan sosial, faktor kebiasaan ibu, dan faktor lingkungan. Prognosis BBLR tergantung dari berat ringannya masa perinatal misalnya masa gestasi (makin muda masa gestasi atau makin rendah berat bayi, makin tinggi angka kematian), asfiksia atau iskemia otak, sindrom gangguan pernafasan, gangguan metabolik. Penelitian ini bertujuan untuk mengetahui hubungan antara umur dan pendidikan ibu dengan kejadian BBLR di Rumah Sakit Umum Pusat Dr. Mohammad Hoesin Palembang Tahun 2010. Penelitian ini menggunakan survey analitik Cross sectional. Populasi penelitian ini adalah semua ibu yang melahirkan di Rumah Sakit Umum Pusat Dr. Mohammad Hoesin Palembang tahun 2010 sebanyak 1.476 ibu melahirkan dengan besar sampel penelitian 94 ibu melahirkan yang diambil dengan tehnik acak sistematik, instrumen penelitian yaitu check list. Analisis data dilakukan secara univariat dan bivariat. Hasil penelitian ini menunjukkan dari 94 ibu didapatkan kejadian BBLR 45 orang (47,9%) yang memiliki umur resiko tinggi 26 kejadian BBLR (27,7%) sedangkan yang pendidikan rendah 52 kejadian BBLR (55,3%). Dari statistik uji Chi-square yang membandingkan p value dengan tingkat kemaknaan α = 0,05 menunjukkan bahwa ada hubungan yang bermakna antara umur ibu p value (0,002) , pendidikan p value (0,003) dengan kejadian BBLR di Rumah Sakit Umum Pusat Dr. Mohammad Hoesin Palembang Tahun 2010. Diharapkan bagi peneliti yang akan datang untuk meneliti lebih mendalam.

Hardy-Weinberg Testing for Continuous Data

Genetics ◽  
1997 ◽  
Vol 147 (4) ◽  
pp. 1965-1975
Author(s):  
Lauren M McIntyre ◽  
B S Weir
Keyword(s):  
Intraclass Correlation ◽  
Kernel Density ◽  
Variable Number ◽  
Continuous Data ◽  
Test Statistic ◽  
Test Procedures ◽  
Chi Square ◽  
Exact Test ◽  
Chi Square Test ◽  
The Many

Abstract Estimation of allelic and genotypic distributions for continuous data using kernel density estimation is discussed and illustrated for some variable number of tandem repeat data. These kernel density estimates provide a useful representation of data when only some of the many variants at a locus are present in a sample. Two Hardy-Weinberg test procedures are introduced for continuous data: a continuous chi-square test with test statistic TCCS and a test based on Hellinger's distance with test statistic TCCS. Simulations are used to compare the powers of these tests to each other and to the powers of a test of intraclass correlation TIC, as well as to the power of Fisher's exact test TFET applied to discretized data. Results indicate that the power of TCCS is better than that of THD but neither is as powerful as TFET. The intraclass correlation test does not perform as well as the other tests examined in this article.

Testing conditional moment restriction models using empirical likelihood

2021 ◽  
Author(s):  
Yves G Berger
Keyword(s):  
Empirical Likelihood ◽  
Model Specification ◽  
Ratio Test ◽  
Conditional Moment ◽  
Nominal Level ◽  
Empirical Likelihood Ratio Test ◽  
Likelihood Model ◽  
Heteroscedastic Errors ◽  
Endogenous Covariates ◽  
The Relationship

Abstract An empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with non-linear endogenous covariates, with or without heteroscedastic errors or non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit studentisation. A simulation study shows that the observed size is close to the nominal level, unlike alternative empirical likelihood approaches. It also offers a major advantages over two-stage least-squares, because the relationship between the endogenous and instrumental variables does not need to be known. An empirical likelihood model specification test is also proposed.

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