Related papers: Yates's MWSM SS in the General Linear Model
It is shown that the sum of squares by Yates's method of weighted squares of means is equivalent to numerator sums of squares formulated by other methods. These relations are established first for hypotheses about fixed effects in a general…
SAS introduced Type III methods to address difficulties in dummy-variable models for effects of multiple factors and covariates. Type III methods are widely used in practice; they are the default method in many statistical computing…
Type III methods were introduced by SAS to address difficulties in dummy-variable models for effects of multiple factors and covariates. They are widely used in practice; they are the default method in several statistical computing…
In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of…
The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…
Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…
This paper proposes new estimators of the number of factors for a generalised factor model with more relaxed assumptions than the strict factor model. Under the framework of large cross-sections $N$ and large time dimensions $T$, we first…
Distorted sums of models were introduced and discussed in [Sh:463]. This notion generalizes the notion of disjoint (or direct) sums of models by letting the summands overlap. In the first section we investigate types in distorted sums and…
Asymmetric causality tests are increasingly gaining popularity in different scientific fields. This approach corresponds better to reality since logical reasons behind asymmetric behavior exist and need to be considered in empirical…
This paper tries to tell the story of the general linear model, which saw the light of day 200 years ago, and the assumptions underlying it. We distinguish three principal stages (ignoring earlier more isolated instances). The model was…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
This paper establishes three properties of F-statistics for inference about the mean vector in multiple regression and analysis of variance. The extra SSE due to imposing a set of linear conditions on the model tests the estimable part of…
Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…
In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…
This article brings attention to some historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to…
In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
Considered here is a hypothesis test for the coefficients in the change-plane regression models to detect the existence of a change plane. The test that is considered is from the class of test problems in which some parameters are not…
In this paper, we analyse the influence of estimating a constant term on the bias of the conditional sum-of-squares (CSS) estimator in a stationary or non-stationary type-II ARFIMA ($p_1$,$d$,$p_2$) model. We derive expressions for the…