摘要:

This note presents a brief overview of the applications of optimization techniques in statistics. Optimizing techniques are broadly classified as classical, variational, numerical, and mathematical programming. A brief discussion of their applications to statistics is given, and a few references are provided for illustrative purposes.

ISSN:0361-0918    

DOI:10.1080/03610917808812079

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

The estimation of a regression function g using linear splines is considered. The integrated mean square error is minimized using choice of estimator, allocation of observations and displacement of knots.

ISSN:0361-0918    

DOI:10.1080/03610917808812080

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

For the portfolio problem with unknown parameter values, we compare the conventional certainty equivalence portfolio choice with the optimal Bayes portfolio. In the important single risky asset case a diffuse Bayes rule leads to portfolios that differ significantly from those suggested by a certainty equivalence rule which we show are inadmissible relative to a quadratic utility function for the range of parameters we consider. These results are invariant to arbitrary changes in the utility function parameters. We illustrate the results using a simple mutual fund example.

ISSN:0361-0918    

DOI:10.1080/03610917808812081

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

In this paper we demonstrate how the task of spectral density estimation by direct methods may be posed as that of solving a simple optimal smoothing problem. A criterion functional is considered which involves a smoothness frequency domain term and a fidelity time domain term.

ISSN:0361-0918    

DOI:10.1080/03610917808812082

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

Recently, the authors and others have made considerable progress in developing algorithms for solving certain large-residual nonlinear least-squares problems where Gauss-Newton (GN) methods can be expected to perform poorly. These methods take account of the term in the Hessian ignored by the GN methods and use quasi-Newton procedures to update this term explicitly. This paper reviews these new approaches and discusses how they can be modified to give good performance on nonlinear models with robust loss functions where lack of scale invariance causes several new problems to arise.

ISSN:0361-0918    

DOI:10.1080/03610917808812083

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

The basis for this paper is in the following observation: for a given “ intractable” optimization problem for which no efficient solution technique exists, if we can devise a systematic procedure for generating independent, heuristic solutions, we should be able to apply statistical extreme-value theory in order to obtain point estimates for the globally optimal solution. This observation has been mechanized in order to evaluate heuristic solutions and assess deviations from optimality, the strategy developed is applicable to a host of combinatorial problems. The assumptions of our model, along with computational experience are discussed.

ISSN:0361-0918    

DOI:10.1080/03610917808812084

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

Selecting an optimal 2k−pfractional factorial is structured as a mathematical programming problem. An algorithm is defined for the solution, and the case of additive costs is shown to have a known solution for resolution III designs.

ISSN:0361-0918    

DOI:10.1080/03610917808812085

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

In geodetic and spatial surveying, accurate statistical es-timates of the Cartesian coordinates of a stationary target depend, in general, on such factors as target position, number and type of instruments, their location, their accuracy, and their mix. Direct measurements are assumed to be made in elevation, azimuth, and range with errors independently and normally distributed. For a mix of instruments, theoretical arguments are established using maximum likelihood estimation to determine the optimal siting of the instruments which minimizes (GDOP)2or the square of the geo-metric dilution of precision = sum of the variances of the estimates in the three orthogonal directions.

ISSN:0361-0918    

DOI:10.1080/03610917808812086

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

For a Wiener-type production process with an observation cost, the optimal stationary strategy is shown to exist. Existence and uniqueness of the optimal strategy is shown by showing that a corresponding contraction mapping has a unique fixed point.

ISSN:0361-0918    

DOI:10.1080/03610917808812087

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

Many optimal curve fitting and approximation problems have the same structure as certain estimation problems involving random processes. This structural correspondence has many useful consequences for curve fitting problems, including recursive algorithms and computable error bounds. The basic facts of this correspondence are reviewed and some new results on error bounds and optimal sampling are presented.

ISSN:0361-0918    

DOI:10.1080/03610917808812088

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor