Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userData-driven efficient score tests for deconvolution problems
122
0
0.0
(
0
)
Added by
Mikhail Langovoy
Publication date
2007
fields
Mathematical Statistics
and research's language is
English
Authors
Mikhail Langovoy
Ask ChatGPT about the research
No Arabic abstract
We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score tests for the case of unknown density. The tests are incorporated with model selection rules to choose reasonable model dimensions automatically by the data. Consistency of the tests is proved.
rate research
Read More
We study the problem of testing the equivalence of functional parameters (such as the mean or variance function) in the two sample functional data problem. In contrast to previous work, which reduces the functional problem to a multiple testing problem for the equivalence of scalar data by comparing the functions at each point, our approach is based on an estimate of a distance measuring the maximum deviation between the two functional parameters. Equivalence is claimed if the estimate for the maximum deviation does not exceed a given threshold. A bootstrap procedure is proposed to obtain quantiles for the distribution of the test statistic and consistency of the corresponding test is proved in the large sample scenario. As the methods proposed here avoid the use of the intersection-union principle they are less conservative and more powerful than the currently available methodology.
We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neymans smooth tests, data-driven score tests, and some types of multi-sample tests as basic examples. Our tests are data-driven and are additionally incorporated with model selection rules. The method allows to use a wide class of model selection rules that are based on the penalization idea. In particular, many of the optimal penalties, derived in statistical literature, can be used in our tests. We establish the behavior of model selection rules and data-driven tests under both the null hypothesis and the alternative hypothesis, derive an explicit detectability rule for alternative hypotheses, and prove a master consistency theorem for the tests from the class. The paper shows that the tests are applicable to a wide range of problems, including hypothesis testing in statistical inverse problems, multi-sample problems, and nonparametric hypothesis testing.
In many applications, the dataset under investigation exhibits heterogeneous regimes that are more appropriately modeled using piece-wise linear models for each of the data segments separated by change-points. Although there have been much work on change point linear regression for the low dimensional case, high-dimensional change point regression is severely underdeveloped. Motivated by the analysis of Minnesota House Price Index data, we propose a fully Bayesian framework for fitting changing linear regression models in high-dimensional settings. Using segment-specific shrinkage and diffusion priors, we deliver full posterior inference for the change points and simultaneously obtain posterior probabilities of variable selection in each segment via an efficient Gibbs sampler. Additionally, our method can detect an unknown number of change points and accommodate different variable selection constraints like grouping or partial selection. We substantiate the accuracy of our method using simulation experiments for a wide range of scenarios. We apply our approach for a macro-economic analysis of Minnesota house price index data. The results strongly favor the change point model over a homogeneous (no change point) high-dimensional regression model.
We consider a testing problem for cross-sectional dependence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional dependence is described through a linear regression model. We study three tests named the sum test, the max test and the max-sum test, where the latter two are new. The sum test is initially proposed by Breusch and Pagan (1980). We design the max and sum tests for sparse and non-sparse residuals in the linear regressions, respectively.And the max-sum test is devised to compromise both situations on the residuals. Indeed, our simulation shows that the max-sum test outperforms the previous two tests. This makes the max-sum test very useful in practice where sparsity or not for a set of data is usually vague. Towards the theoretical analysis of the three tests, we have settled two conjectures regarding the sum of squares of sample correlation coefficients asked by Pesaran (2004 and 2008). In addition, we establish the asymptotic theory for maxima of sample correlations coefficients appeared in the linear regression model for panel data, which is also the first successful attempt to our knowledge. To study the max-sum test, we create a novel method to show asymptotic independence between maxima and sums of dependent random variables. We expect the method itself is useful for other problems of this nature. Finally, an extensive simulation study as well as a case study are carried out. They demonstrate advantages of our proposed methods in terms of both empirical powers and robustness for residuals regardless of sparsity or not.
Penalization procedures often suffer from their dependence on multiplying factors, whose optimal values are either unknown or hard to estimate from the data. We propose a completely data-driven calibration algorithm for this parameter in the least-squares regression framework, without assuming a particular shape for the penalty. Our algorithm relies on the concept of minimal penalty, recently introduced by Birge and Massart (2007) in the context of penalized least squares for Gaussian homoscedastic regression. On the positive side, the minimal penalty can be evaluated from the data themselves, leading to a data-driven estimation of an optimal penalty which can be used in practice; on the negative side, their approach heavily relies on the homoscedastic Gaussian nature of their stochastic framework. The purpose of this paper is twofold: stating a more general heuristics for designing a data-driven penalty (the slope heuristics) and proving that it works for penalized least-squares regression with a random design, even for heteroscedastic non-Gaussian data. For technical reasons, some exact mathematical results will be proved only for regressogram bin-width selection. This is at least a first step towards further results, since the approach and the method that we use are indeed general.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
