21,280 research outputs found
Nonparametric Measure of Linear Trend
This paper proposes and develops a nonparametric statistical procedure for estimating linear trend effect on data using nonparametric regression methods based on ranks, assuming one of the sampled populations is a measurement on a time scale. The populations of interest may be measurements on as low as the ordinal scale. The nonparametric regression-based linear trend estimate is shown to be similar in computation to the Spearman’s Rank Correlation Coefficient. Test statistics are developed for testing hypotheses on the linear trend effect. Sample data are used to illustrate the proposed method. Keywords: Nonparametric, Linear, Test Statistic, Measure, Trend, Rati
Smoothing-inspired lack-of-fit tests based on ranks
A rank-based test of the null hypothesis that a regressor has no effect on a
response variable is proposed and analyzed. This test is identical in structure
to the order selection test but with the raw data replaced by ranks. The test
is nonparametric in that it is consistent against virtually any smooth
alternative, and is completely distribution free for all sample sizes. The
asymptotic distribution of the rank-based order selection statistic is obtained
and seen to be the same as that of its raw data counterpart. Exact small sample
critical values of the test statistic are provided as well. It is shown that
the Pitman-Noether efficiency of the proposed rank test compares very favorably
with that of the order selection test. In fact, their asymptotic relative
efficiency is identical to that of the Wilcoxon signed rank and -tests. An
example involving microarray data illustrates the usefulness of the rank test
in practice.Comment: Published in at http://dx.doi.org/10.1214/193940307000000103 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Adaptive goodness-of-fit tests based on signed ranks
Within the nonparametric regression model with unknown regression function
and independent, symmetric errors, a new multiscale signed rank statistic
is introduced and a conditional multiple test of the simple hypothesis
against a nonparametric alternative is proposed. This test is distribution-free
and exact for finite samples even in the heteroscedastic case. It adapts in a
certain sense to the unknown smoothness of the regression function under the
alternative, and it is uniformly consistent against alternatives whose sup-norm
tends to zero at the fastest possible rate. The test is shown to be
asymptotically optimal in two senses: It is rate-optimal adaptive against
H\"{o}lder classes. Furthermore, its relative asymptotic efficiency with
respect to an asymptotically minimax optimal test under sup-norm loss is close
to 1 in case of homoscedastic Gaussian errors within a broad range of
H\"{o}lder classes simultaneously.Comment: Published in at http://dx.doi.org/10.1214/009053607000000992 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
An Empirical Analysis of the Canadian Budget Process
This paper provides a statistical analysis of the forecasts of significant number of expenditure and revenue components of the Federal budget provided each year by the Department of Finance. The sample available for such an investigation is limited and we describe an easily-applied nonparametric testing methodology which is more appropriate than the usual regression-based approach in small samples. The reliability and relative power of the various nonparametric tests are illustrated in a series of simulations. Applying these tests to the fiscal forecasts, we find that there is little cause to be concerned with the forecast performance of the Department of Finance over the last seventeen years.
Dans cette étude nous examinons les erreurs de prévisions pour les comptes de dépenses et recettes du budget canadien. Nous appliquons des méthodes non-paramétriques à cause des petites tailles d'échantillons. Nous trouvons peu d'erreurs systématiques dans les prévisions budgétaires.Budget forecast; Nonparametric methods, Prévisions budgétaires ; Méthodes non-paramétriques
Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks
We present a novel Bayesian nonparametric regression model for covariates X
and continuous, real response variable Y. The model is parametrized in terms of
marginal distributions for Y and X and a regression function which tunes the
stochastic ordering of the conditional distributions F(y|x). By adopting an
approximate composite likelihood approach, we show that the resulting posterior
inference can be decoupled for the separate components of the model. This
procedure can scale to very large datasets and allows for the use of standard,
existing, software from Bayesian nonparametric density estimation and
Plackett-Luce ranking estimation to be applied. As an illustration, we show an
application of our approach to a US Census dataset, with over 1,300,000 data
points and more than 100 covariates
Novel statistical approaches for non-normal censored immunological data: analysis of cytokine and gene expression data
Background: For several immune-mediated diseases, immunological analysis will become more complex in the future with datasets in which cytokine and gene expression data play a major role. These data have certain characteristics that require sophisticated statistical analysis such as strategies for non-normal distribution and censoring. Additionally, complex and multiple immunological relationships need to be adjusted for potential confounding and interaction effects.
Objective: We aimed to introduce and apply different methods for statistical analysis of non-normal censored cytokine and gene expression data. Furthermore, we assessed the performance and accuracy of a novel regression approach in order to allow adjusting for covariates and potential confounding.
Methods: For non-normally distributed censored data traditional means such as the Kaplan-Meier method or the generalized Wilcoxon test are described. In order to adjust for covariates the novel approach named Tobit regression on ranks was introduced. Its performance and accuracy for analysis of non-normal censored cytokine/gene expression data was evaluated by a simulation study and a statistical experiment applying permutation and bootstrapping.
Results: If adjustment for covariates is not necessary traditional statistical methods are adequate for non-normal censored data. Comparable with these and appropriate if additional adjustment is required, Tobit regression on ranks is a valid method. Its power, type-I error rate and accuracy were comparable to the classical Tobit regression.
Conclusion: Non-normally distributed censored immunological data require appropriate statistical methods. Tobit regression on ranks meets these requirements and can be used for adjustment for covariates and potential confounding in large and complex immunological datasets
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