Statistical hypothesis testing

About: Statistical hypothesis testing is a research topic. Over the lifetime, 19580 publications have been published within this topic receiving 1037815 citations. The topic is also known as: statistical hypothesis testing & confirmatory data analysis.

Goodness of Fit and Related Inference Processes for Quantile Regression

Abstract: We introduce a goodness-of-fit process for quantile regression analogous to the conventional R2 statistic of least squares regression. Several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated. The asymptotic behavior of the inference processes is shown to be closely related to earlier p-sample goodness-of-fit theory involving Bessel processes. The approach is illustrated with some hypothetical examples, an application to recent empirical models of international economic growth, and some Monte Carlo evidence.

The Robustness of Critical Period Effects in Second Language Acquisition.

Abstract: This study was designed to test the Fundamental Difference Hypothesis (Bley-Vroman, 1988), which states that, whereas children are known to learn language almost completely through (implicit) domain-specific mechanisms, adults have largely lost the ability to learn a language without reflecting on its structure and have to use alternative mechanisms, drawing especially on their problem-solving capacities, to learn a second language. The hypothesis implies that only adults with a high level of verbal analytical ability will reach near-native competence in their second language, but that this ability will not be a significant predictor of success for childhood second language acquisition. A study with 57 adult Hungarian-speaking immigrants confirmed the hypothesis in the sense that very few adult immigrants scored within the range of child arrivals on a grammaticality judgment test, and that the few who did had high levels of verbal analytical ability; this ability was not a significant predictor for childhood arrivals. This study replicates the findings of Johnson and Newport (1989) and provides an explanation for the apparent exceptions in their study. These findings lead to a reconceptualization of the Critical Period Hypothesis: If the scope of this hypothesis is limited to implicit learning mechanisms, then it appears that there may be no exceptions to the age effects that the hypothesis seeks to explain.

Tests for Parameter Instability in Regressions With I(1) Processes

Abstract: This article derives the large-sample distributions of Lagrange multiplier (LM) tests for parameter instability against several alternatives of interest in the context of cointegrated regression models. The fully modified estimator of Phillips and Hansen is extended to cover general models with stochastic and deterministic trends. The test statistics considered include the SupF test of Quandt, as well as the LM tests of Nyblom and of Nabeya and Tanaka. It is found that the asymptotic distributions depend on the nature of the regressor processes—that is, if the regressors are stochastic or deterministic trends. The distributions are noticeably different from the distributions when the data are weakly dependent. It is also found that the lack of cointegration is a special case of the alternative hypothesis considered (an unstable intercept), so the tests proposed here may also be viewed as a test of the null of cointegration against the alternative of no cointegration. The tests are applied to three data se...

Parameter Estimation and Hypothesis Testing in Linear Models

Abstract: This textbook on theoretical geodesy deals with the estimation of unknown parameters, the testing of hypothesis and the estimation of intervals in linear models. The reader will find presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model, as well as the mixed model for estimation random parameters. To make the book self-contained most of the necessary theorems of vector and matrix-algebra and the probability distributions for the test statistics are derived. Students of geodesy, as well as of mathematics and engineering, will find the geodetical application of mathematical and statistical models extremely useful.

Testing for a Unit Root in a Time Series With a Changing Mean

Abstract: This study considers testing for a unit root in a time series characterized by a structural change in its mean level. My approach follows the “intervention analysis” of Box and Tiao (1975) in the sense that I consider the change as being exogenous and as occurring at a known date. Standard unit-root tests are shown to be biased toward nonrejection of the hypothesis of a unit root when the full sample is used. Since tests using split sample regressions usually have low power, I design test statistics that allow the presence of a change in the mean of the series under both the null and alternative hypotheses. The limiting distribution of the statistics is derived and tabulated under the null hypothesis of a unit root. My analysis is illustrated by considering the behavior of various univariate time series for which the unit-root hypothesis has been advanced in the literature. This study complements that of Perron (1989), which considered time series with trends.