scholarly journals Field Significance of Regression Patterns

2011 ◽  
Vol 24 (19) ◽  
pp. 5094-5107 ◽  
Author(s):  
Timothy DelSole ◽  
Xiaosong Yang
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Significance Test ◽  
Spatial Filter ◽  
Climate Index ◽  
Boreal Winter ◽  
Ratio Test ◽  
Test Statistic ◽  
Canonical Correlations ◽  
The Cross

Regression patterns often are used to diagnose the relation between a field and a climate index, but a significance test for the pattern “as a whole” that accounts for the multiplicity and interdependence of the tests has not been widely available. This paper argues that field significance can be framed as a test of the hypothesis that all regression coefficients vanish in a suitable multivariate regression model. A test for this hypothesis can be derived from the generalized likelihood ratio test. The resulting statistic depends on relevant covariance matrices and accounts for the multiplicity and interdependence of the tests. It also depends only on the canonical correlations between the predictors and predictands, thereby revealing a fundamental connection to canonical correlation analysis. Remarkably, the test statistic is invariant to a reversal of the predictors and predictands, allowing the field significance test to be reduced to a standard univariate hypothesis test. In practice, the test cannot be applied when the number of coefficients exceeds the sample size, reflecting the fact that testing more hypotheses than data is ill conceived. To formulate a proper significance test, the data are represented by a small number of principal components, with the number chosen based on cross-validation experiments. However, instead of selecting the model that minimizes the cross-validated mean square error, a confidence interval for the cross-validated error is estimated and the most parsimonious model whose error is within the confidence interval of the minimum error is chosen. This procedure avoids selecting complex models whose error is close to much simpler models. The procedure is applied to diagnose long-term trends in annual average sea surface temperature and boreal winter 300-hPa zonal wind. In both cases a statistically significant 50-yr trend pattern is extracted. The resulting spatial filter can be used to monitor the evolution of the regression pattern without temporal filtering.

Hypothesis Testing

2005 ◽  
Author(s):  
D. Brynn Hibbert ◽  
J. Justin Gooding
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Hypothesis Test ◽  
Significance Test ◽  
Type I ◽  
Test Statistic ◽  
The Difference ◽  
Set Up ◽  
Type Ii Errors ◽  
Normally Distributed

• To understand the concept of the null hypothesis and the role of Type I and Type II errors. • To test that data are normally distributed and whether a datum is an outlier. • To determine whether there is systematic error in the mean of measurement results. • To perform tests to compare the means of two sets of data.… One of the uses to which data analysis is put is to answer questions about the data, or about the system that the data describes. In the former category are ‘‘is the data normally distributed?’’ and ‘‘are there any outliers in the data?’’ (see the discussions in chapter 1). Questions about the system might be ‘‘is the level of alcohol in the suspect’s blood greater than 0.05 g/100 mL?’’ or ‘‘does the new sensor give the same results as the traditional method?’’ In answering these questions we determine the probability of finding the data given the truth of a stated hypothesis—hence ‘‘hypothesis testing.’’ A hypothesis is a statement that might, or might not, be true. Usually the hypothesis is set up in such a way that it is possible to calculate the probability (P) of the data (or the test statistic calculated from the data) given the hypothesis, and then to make a decision about whether the hypothesis is to be accepted (high P) or rejected (low P). A particular case of a hypothesis test is one that determines whether or not the difference between two values is significant—a significance test. For this case we actually put forward the hypothesis that there is no real difference and the observed difference arises from random effects: it is called the null hypothesis (H<sub>0</sub>). If the probability that the data are consistent with the null hypothesis falls below a predetermined low value (say 0.05 or 0.01), then the hypothesis is rejected at that probability. Therefore, p<0.05 means that if the null hypothesis were true we would find the observed data (or more accurately the value of the statistic, or greater, calculated from the data) in less than 5% of repeated experiments.

Non-Standard Tests through a Composite Null and Alternative in Point-Identified Parameters

2015 ◽  
Vol 4 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Jinyong Hahn ◽  
Geert Ridder
Keyword(s):  
Confidence Interval ◽  
Alternative Hypothesis ◽  
Tuning Parameter ◽  
Closed Form Expression ◽  
Ratio Test ◽  
Population Parameters ◽  
Test Statistic ◽  
Inference Problem ◽  
New Approach ◽  
Interval Censored

AbstractWe propose a new approach to statistical inference on parameters that depend on population parameters in a non-standard way. As examples we consider a parameter that is interval identified and a parameter that is the maximum (or minimum) of population parameters. In both examples we transform the inference problem into a test of a composite null against a composite alternative hypothesis involving point identified population parameters. We use standard tools in this testing problem. This setup substantially simplifies the conceptual basis of the inference problem. By inverting the Likelihood Ratio test statistic for the composite null and composite alternative inference problem, we obtain a closed form expression for the confidence interval that does not require any tuning parameter and is uniformly valid. We use our method to derive a confidence interval for a regression coefficient in a multiple linear regression with an interval censored dependent variable.

scholarly journals Learning Attribute Hierarchies From Data: Two Exploratory Approaches

2020 ◽  
pp. 107699862093109
Author(s):  
Chun Wang ◽  
Jing Lu
Keyword(s):  
Latent Variable ◽  
Latent Class ◽  
Hypothesis Test ◽  
Structural Features ◽  
Classification Model ◽  
Ratio Test ◽  
Test Statistic ◽  
Reference Distribution ◽  
Fine Grained ◽  
Log Linear

In cognitive diagnostic assessment, multiple fine-grained attributes are measured simultaneously. Attribute hierarchies are considered important structural features of cognitive diagnostic models (CDMs) that provide useful information about the nature of attributes. Templin and Bradshaw first introduced a hierarchical diagnostic classification model (HDCM) that directly takes into account attribute hierarchies, and hence, HDCM is nested within more general CDMs. They also formulated an empirically driven hypothesis test to statistically test one hypothesized link (between two attributes) at a time. However, their likelihood ratio test statistic does not have a known reference distribution, so it is cumbersome to perform hypothesis testing at scale. In this article, we studied two exploratory approaches that could learn the attribute hierarchies directly from data, namely, the latent variable selection (LVS) approach and the regularized latent class modeling (RLCM) approach. An identification constraint was proposed for the LVS approach. Simulation results revealed that both approaches could successfully identify different types of attribute hierarchies, when the underlying CDM is either the deterministic input noisy and gate model or the saturated log-linear CDM. The LVS approach outperformed the RLCM approach, especially when the total number of attributes increases.

scholarly journals Changes in Cytomegalovirus Seroprevalence Among U.S. Children Aged 1–5 Years: The National Health and Nutrition Examination Surveys

2020 ◽  
Author(s):  
Molly R Petersen ◽  
Eshan U Patel ◽  
Alison G Abraham ◽  
Thomas C Quinn ◽  
Aaron A R Tobian
Keyword(s):  
Confidence Interval ◽  
National Health ◽  
Immunoglobulin G ◽  
Igg Antibodies ◽  
Cross Sectional ◽  
Health And Nutrition ◽  
Prevalence Difference ◽  
The Cross ◽  
Us Children

Abstract Data from the cross-sectional National Health and Nutrition Examination Surveys (NHANES) indicate that the seroprevalence of cytomegalovirus immunoglobulin G (IgG) antibodies among US children aged 1–5 years was 20.7% (95% confidence interval [CI]: 14.0, 29.0) in 2011–2012 and 28.2% (95% CI: 23.1–34.0) in 2017–2018 (adjusted prevalence difference, +7.6% [95% CI: −.4, +15.6]).

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

On “Field Significance” and the False Discovery Rate

2006 ◽  
Vol 45 (9) ◽  
pp. 1181-1189 ◽  
Author(s):  
D. S. Wilks
Keyword(s):  
False Discovery Rate ◽  
Statistical Power ◽  
Statistical Significance ◽  
Significance Test ◽  
P Value ◽  
Test Statistic ◽  
Global Test ◽  
Additional Advantage ◽  
Counting Procedure ◽  
False Discovery

Abstract The conventional approach to evaluating the joint statistical significance of multiple hypothesis tests (i.e., “field,” or “global,” significance) in meteorology and climatology is to count the number of individual (or “local”) tests yielding nominally significant results and then to judge the unusualness of this integer value in the context of the distribution of such counts that would occur if all local null hypotheses were true. The sensitivity (i.e., statistical power) of this approach is potentially compromised both by the discrete nature of the test statistic and by the fact that the approach ignores the confidence with which locally significant tests reject their null hypotheses. An alternative global test statistic that has neither of these problems is the minimum p value among all of the local tests. Evaluation of field significance using the minimum local p value as the global test statistic, which is also known as the Walker test, has strong connections to the joint evaluation of multiple tests in a way that controls the “false discovery rate” (FDR, or the expected fraction of local null hypothesis rejections that are incorrect). In particular, using the minimum local p value to evaluate field significance at a level αglobal is nearly equivalent to the slightly more powerful global test based on the FDR criterion. An additional advantage shared by Walker’s test and the FDR approach is that both are robust to spatial dependence within the field of tests. The FDR method not only provides a more broadly applicable and generally more powerful field significance test than the conventional counting procedure but also allows better identification of locations with significant differences, because fewer than αglobal × 100% (on average) of apparently significant local tests will have resulted from local null hypotheses that are true.

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