Stochastic Expansions and Asymptotic Approximations

1992 ◽  
Vol 8 (3) ◽  
pp. 343-367 ◽  
Author(s):  
Michael A. Magdalinos
Keyword(s):  
Distribution Function ◽  
Asymptotic Approximation ◽  
Asymptotic Methods ◽  
Asymptotic Approximations ◽  
Test Statistic ◽  
Chi Square ◽  
Stochastic Expansion ◽  
Stochastic Expansions ◽  
General Conditions

Under general conditions the distribution function of the first few terms in a stochastic expansion of an econometric estimator or test statistic provides an asymptotic approximation to the distribution function of the original estimator or test statistic with an error of order less than that of the limiting normal or chi-square approximation. This can be used to establish the validity of several refined asymptotic methods, including the comparison of Nagar-type moments and the use of formal Edgeworth or Edgeworth-type approximations.

scholarly journals UNIFORM ASYMPTOTIC APPROXIMATIONS FOR THE MEIXNER–SOBOLEV POLYNOMIALS

2012 ◽  
Vol 10 (03) ◽  
pp. 345-361 ◽  
Author(s):  
S. FARID KHWAJA ◽  
A. B. OLDE DAALHUIS
Keyword(s):  
Integral Representation ◽  
Asymptotic Approximation ◽  
Hypergeometric Functions ◽  
Sobolev Class ◽  
Asymptotic Methods ◽  
Asymptotic Approximations ◽  
Limit Case ◽  
Airy Functions ◽  
Meixner Polynomials ◽  
First Time

We obtain uniform asymptotic approximations for the monic Meixner–Sobolev polynomials Sn(x). These approximations for n → ∞, are uniformly valid for x/n restricted to certain intervals, and are in terms of Airy functions. We also give asymptotic approximations for the location of the zeros of Sn(x), especially the small and the large zeros are discussed. As a limit case, we also give a new asymptotic approximation for the large zeros of the classical Meixner polynomials. The method is based on an integral representation in which a hypergeometric function appears in the integrand. After a transformation, the hypergeometric functions can be uniformly approximated by unity, and all that remains are simple integrals for which standard asymptotic methods are used. As far as we are aware, this is the first time that standard uniform asymptotic methods have been used for the Sobolev-class of orthogonal polynomials.

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.

Investigating association between factors fostering attention to a stock and rationales to buy it: an empirical analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ripsy Bondia ◽  
Pratap C. Biswal ◽  
Abinash Panda
Keyword(s):  
Decision Making ◽  
Categorical Data ◽  
Categorical Variables ◽  
Individual Investors ◽  
Multiple Response ◽  
Individual Investor ◽  
Test Statistic ◽  
Chi Square ◽  
Content Type ◽  
First Order

PurposeCan something that drives our initial attention toward a stock have any implications on final decision to buy it? This paper empirically and statistically tests association, if any, between factors fostering attention toward a stock and rationales to buy it.Design/methodology/approachThis paper uses survey responses of individual investors involving multiple response categorical data. Association between attention fostering factors and rationales is tested using a modified first-order corrected Rao-Scott chi-square test statistic (to adjust for within-participant dependence among responses in case of multiple response categorical variables). Further, odds ratios and mosaic plots are used to determine the effect size of association.FindingsStrong association is seen between attention fostering factors and rationales to buy a stock. Further, strongest associations are seen in cases where origin is the same underlying influencing factor. Some of the most cited attention fostering factors and rationales in this research stem from familiarity bias and expert bias.Practical implicationsWhat starts as a trivial attention fostering factor, which may not even be recognized by majority investors, can go on to become one of the rationales for buying a stock. This can result in substantial financial implications for an individual investor. Investor education agencies and regulatory authorities can make investors cognizant of such association, which can help investors to improve and adjust their decision making accordingly.Originality/valueThe extant literature discusses factors/biases influencing buying decisions of individual investors. This research takes a step ahead by distinguishing these factors in terms of whether they play role of (1) fostering attention toward a stock or (2) of reasons for ultimately buying it. Such dissection of factors/biases, to the best of authors' knowledge, has not been done previously in any empirical and statistical analysis. The paper uses multiple response categorical data and applies a modified first-order corrected Rao-Scott chi-square statistic to test association. Application of the above-mentioned test statistic has not been done previously in context of individual investor decision-making.

scholarly journals Guía De Evaluación Por Resultados En El Aprendizaje De Cinemática Y Su Incidencia En El Rendimiento De Los Estudiantes De Ingeniería En Biotecnología Ambiental

2018 ◽  
Vol 14 (33) ◽  
pp. 331
Author(s):  
Pumalema Morocho Blanca Fabiola ◽  
Borja Saavedra Myrian Cecilia ◽  
Cuadrado Pumalema Coralia Fabiola
Keyword(s):  
Research Problem ◽  
Curriculum Theory ◽  
Test Statistic ◽  
Chi Square ◽  
First Semester ◽  
Evaluation Approach ◽  
Academic Activities ◽  
Chi Square Test ◽  
Experimental Group ◽  
Kinematics Learning

The objective of the research was to analyze the most appropriate approach to evaluate kinematics learning of first semester students in Engineering Environmental Biotechnology School of Chemical Sciences at the Escuela Superior Politecnica of Chimborazo. To do this, a theoretical framework was established based on didactics and curriculum theory. The investigation was correlational, explanatory and field. The Delphi method was used for consult of experts, who contributed synergistically to give a suitable answer to the research problem. A non-random sample of 24 students from a population of 68 was considered. To test the specific hypotheses, the Chi-square test statistic was used determining that the most appropriate kinematics evaluation approach to apply in the experimental group is by results through indicators of cognitive and affective domain, which positively affects the performance of students in the context of research. Because evaluation is a learning tool and an action-oriented organizational process to improve academic activities and obtain better results in the future, it is recommended to contrast evaluation by learning outcomes with evaluation by objectives or competences.

scholarly journals Profile Inferences on Restricted Additive Partially Linear EV Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiuli Wang
Keyword(s):  
Least Squares ◽  
Asymptotic Distribution ◽  
The Other ◽  
Finite Sample ◽  
Test Statistic ◽  
Two Stage ◽  
Chi Square ◽  
Partially Linear ◽  
Profile Least Squares ◽  
Restricted Estimator

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

Asymptotic stepwise solutions of the Korteweg--de Vries equation with a singular perturbation and their accuracy

2021 ◽  
Vol 8 (3) ◽  
pp. 410-421
Author(s):  
S. I. Lyashko ◽  
◽  
V. H. Samoilenko ◽  
Yu. I. Samoilenko ◽  
I. V. Gapyak ◽  
...  
Keyword(s):  
Singular Perturbation ◽  
Small Parameter ◽  
Asymptotic Approximation ◽  
Vries Equation ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Main Term ◽  
Asymptotic Approximations ◽  
De Vries ◽  
The Given

The paper deals with the Korteweg-de Vries equation with variable coefficients and a small parameter at the highest derivative. The asymptotic step-like solution to the equation is obtained by the non-linear WKB technique. An algorithm of constructing the higher terms of the asymptotic step-like solutions is presented. The theorem on the accuracy of the higher asymptotic approximations is proven. The proposed technique is demonstrated by example of the equation with given variable coefficients. The main term and the first asymptotic approximation of the given example are found, their analysis is done and statement of the approximate solutions accuracy is presented.

Testing for individual sphericity in heterogeneous panels

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 740-747
Author(s):  
Simon A Broda
Keyword(s):  
Distribution Function ◽  
Normal Approximation ◽  
Empirical Work ◽  
Null Distribution ◽  
Saddlepoint Approximation ◽  
Test Statistic ◽  
Cross Sectional ◽  
P Values ◽  
Cross Sectional Dimension ◽  
Heterogeneous Panels

Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.

On a point process with independent locations

1975 ◽  
Vol 12 (3) ◽  
pp. 435-446 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Distribution Function ◽  
Point Process ◽  
Point Processes ◽  
Random Variables ◽  
Independent Random Variables ◽  
General Conditions

A class of point processes is considered, in which the locations of the points are independent random variables. In particular some properties of the process in which the distribution function of the position of the nth event is the n-fold convolution of some distribution function F, are investigated. It is shown that, under fairly general conditions, the process remote from the origin will be asymptotically Poisson. It is also shown that the variance of the number of events in the interval (0, t] is . Some generalisations are discussed.

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