Eigenvalue—Free methods for computing the distribution of a quadratic form in normal variables

The traditional method for computing the distribution of a quadratic form in normal variables, Pr(v'Qv相似文献   

Further mnemonics for the Kalman filter updating formulas

In this paper the author supplements his earlier work on the covariance matrix updating formulas of the Kalman filter by supplying mnemonics for the conditional mean updating formulas.     

Testing linear inequality constraints in the standard linear model

In this paper we are concerned with the problem of testing whether the â-parameters of the standard linear model satisfy the linear equality constraints R = r when they are known to satisfy the corresponding linear inequality constraints Râ ? r. In particular we will show that the exact finite sample null distributions of the Likelihood Ratio, Wald and Kuhn-Tucker

statistics are known when R is of full row rank but not known when R has less than full row rank. The less than full row rank problem has not been discussed previously but it is of considerable potential importance.

This paper contains several simple numerical examples which illustrate the computational details of the tests     

An examination of recent criticisms of ridge regression simulation designs

In this paper we carefully examine three propositions asserting that certain simulation studies are biased in favour of ridge regression and find them to be ill-founded.     

A genealogy of Florence Nightingale, Charles Darwin, Francis Galton and Francis Ysidro Edgeworth with special reference to their Italian connections and an annexe on Beatrice Webb and Charles Booth

In this article we show that several leading natural scientists, statisticians and social scientists born between 1730 and 1930 are closely related by marriage, thereby forming what Annan (Studies in social history: a tribute to C. M. Trevelyan, Longmans, Green, London, pp 241–287, 1955) has named an Intellectual Aristocracy. We also establish that the first three individuals mentioned in our title had family connections with Italy.     

Unbiased L1 and L∞ estimation

Sielken and Heartely 1973 have shown that the L₁ and L_∞ estimation problems may be formulated in such a way as to yield unbiased estimators of in the standard linear model y = Xβ + ε In this paper we will show that the L₁ estimation problem is closely related to the dual of the L_∞ estimation problem and vice versa. We will use this resu;t to obtain four fistiner lineat programming problems which yield unbiased L₁ and L_∞ estimators of β.     

Relative local influence and the condition number

In this paper we show that the condition number traditionally used by numerical analysts is closely related to a variant of Cook's (1986) absolute measure of local influence. The nature of the assumptions made in our derivation of this result raises several questions concerning the relevance of the traditional condition number as a measure of computational accuracy in statistical studies.     

Some Early Work on the Duality Between Points and Lines

In this paper we will show that certain features of the type of duality recently discussed by Souvaine and Steele (1987) and Owen and Shiau (1988) may be traced in the earlier work of Laplace (1786), Newcomb (1873a, b) and Edgeworth (1888).     

A critique of recent methods for computing the distribution of the Durbin-Watson and other invariant test statistics

In recent papers Ansley, Kohn and Shively (SAK, 1990; AKS, 1992; KSA, 1993) have proposed methods for evaluating the null distribution of the Durbin-Watson and related statistics more rapidly than by the methods of Davies (1980) or Farebrother (1980, 1990). In this paper we discuss several problems concerning the numerical accuracy of these new procedures and recommend that practitioners intending to use them should do so with caution.