ترغب بنشر مسار تعليمي؟ اضغط هنا

The Measurement of Statistical Evidence as the Basis for Statistical Reasoning

118   0   0.0 ( 0 )
 نشر من قبل Michael Evans
 تاريخ النشر 2019
  مجال البحث الاحصاء الرياضي
والبحث باللغة English
 تأليف Michael Evans




اسأل ChatGPT حول البحث

There are various approaches to the problem of how one is supposed to conduct a statistical analysis. Different analyses can lead to contradictory conclusions in some problems so this is not a satisfactory state of affairs. It seems that all approaches make reference to the evidence in the data concerning questions of interest as a justification for the methodology employed. It is fair to say, however, that none of the most commonly used methodologies is absolutely explicit about how statistical evidence is to be characterized and measured. We will discuss the general problem of statistical reasoning and the development of a theory for this that is based on being precise about statistical evidence. This will be shown to lead to the resolution of a number of problems.

قيم البحث

اقرأ أيضاً

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, chec king the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm.
229 - Song Xi Chen , Liuhua Peng 2018
This paper considers distributed statistical inference for general symmetric statistics %that encompasses the U-statistics and the M-estimators in the context of massive data where the data can be stored at multiple platforms in different locations. In order to facilitate effective computation and to avoid expensive communication among different platforms, we formulate distributed statistics which can be conducted over smaller data blocks. The statistical properties of the distributed statistics are investigated in terms of the mean square error of estimation and asymptotic distributions with respect to the number of data blocks. In addition, we propose two distributed bootstrap algorithms which are computationally effective and are able to capture the underlying distribution of the distributed statistics. Numerical simulation and real data applications of the proposed approaches are provided to demonstrate the empirical performance.
In this paper we consider the linear regression model $Y =S X+varepsilon $ with functional regressors and responses. We develop new inference tools to quantify deviations of the true slope $S$ from a hypothesized operator $S_0$ with respect to the Hi lbert--Schmidt norm $| S- S_0|^2$, as well as the prediction error $mathbb{E} | S X - S_0 X |^2$. Our analysis is applicable to functional time series and based on asymptotically pivotal statistics. This makes it particularly user friendly, because it avoids the choice of tuning parameters inherent in long-run variance estimation or bootstrap of dependent data. We also discuss two sample problems as well as change point detection. Finite sample properties are investigated by means of a simulation study. Mathematically our approach is based on a sequential version of the popular spectral cut-off estimator $hat S_N$ for $S$. It is well-known that the $L^2$-minimax rates in the functional regression model, both in estimation and prediction, are substantially slower than $1/sqrt{N}$ (where $N$ denotes the sample size) and that standard estimators for $S$ do not converge weakly to non-degenerate limits. However, we demonstrate that simple plug-in estimators - such as $| hat S_N - S_0 |^2$ for $| S - S_0 |^2$ - are $sqrt{N}$-consistent and its sequenti
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we derive th e joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, i.e., the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample size are comparably large. In general, the joint distribution is given in terms of linear combinations of finitely many Gaussian and Chi-square variables, with parameters depending on the projection direction and the spikes. Our assumption on the spikes is fully general. First, the strengths of spikes are only required to be slightly above the critical threshold and no upper bound on the strengths is needed. Second, multiple spikes, i.e., spikes with the same strength, are allowed. Third, no structural assumption is imposed on the spikes. Thanks to the general setting, we can then apply the results to various high dimensional statistical hypothesis testing problems involving both the eigenvalues and eigenvectors. Specifically, we propose accurate and powerful statistics to conduct hypothesis testing on the principal components. These statistics are data-dependent and adaptive to the underlying true spikes. Numerical simulations also confirm the accuracy and powerfulness of our proposed statistics and illustrate significantly better performance compared to the existing methods in the literature. Especially, our methods are accurate and powerful even when either the spikes are small or the dimension is large.
Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics by Kou, Zhou and Wong [math.ST/0507080]
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا