On theE-optimality of certain asymmetrical designs under mixed effects model

TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established.

1. A group divisible design with λ₂ = λ₁ + 1.
2. A group divisible design with λ₁ = λ₂ + 1 and group size 2.
3. A linked block design.
4. The dual of design (i)
5. The dual of design (ii).

All these designs are known to satisfy the same optimality property under fixed effects model whenk<v, while the design (i) is known to beE-optimal even whenk>v. From the results proved here, theE-optimality of designs (ii, (iii), (iv) and (v) under fixed effects model in the situation whenk >v also follows.     

On the E-optimality of truncated block designs

Sufficient conditions are found for designs, derived from completely symmetric designs by deleting binary blocks, to be E-optimal. Sufficient conditions are also found for E-optimality of designs obtained from other E-optimal designs by deleting all blocks forming a balanced incomplete block design on a subset of the treatments. The results include many binary and non-binary designs for which E-optimality was previously unknown.     

Optimal variance- and efficiency-balanced designs for one- and two-way elimination of heterogeneity

Summary In this paper, a series ofE-optimal non-binary variance balanced (block or row-column) designs and a series ofE-optimal non-binary efficiency balanced (block or row-column) designs are provided in certain broad classes of competing designs. Furthermore, their high efficiencies by the usualA- andD-optimality criteria are shown.     

Totally positive regression: E-optimal designs

E-optimality of approximate designs in linear regression models is paired with a dual problem of nonlinear Chebyshev approximation. When the regression functions form a totally positive system, then the information matrices of designs for subparameters turn out to be “almost” totally positive, a property which allows to solve the nonlinear Chebyshev problem. Thereby we obtain explicit formulae for E-optimal designs in terms of equi-oscillating generalized polynomials. The considerations unify and generalize known results on E-optimality for particular regression setups.     

On someE-optimal block designs

Summary TheE-optimality of block designs is the concern of this paper. Bounds for the smallest positive eigenvalue of theC-matrix of block designs are obtained in some general classes of connected designs with equal or unequal block sizes. Use of these bounds is made to obtainE-optimal block designs in various classes.     

R-optimal designs for multi-factor models with heteroscedastic errors

In this paper, we consider the R-optimal design problem for multi-factor regression models with heteroscedastic errors. It is shown that a R-optimal design for the heteroscedastic Kronecker product model is given by the product of the R-optimal designs for the marginal one-factor models. However, R-optimal designs for the additive models can be constructed from R-optimal designs for the one-factor models only if sufficient conditions are satisfied. Several examples are presented to illustrate and check optimal designs based on R-optimality criterion.     

A class of non binary unequally replicatedE-optimal designs

In a situation where the given set of parameters (b, k andv) precludes the existence of any known optimal block designs, but an optimal block design is known to exist with parametersb, k andv*>v, a new design is shown to be useful. This (b, k, v) design is obtained from the (b, k, v*) optimal design by collapsing the classes of a suitable paritition of the treatment set (of the latter design) to treatments (of the former). We call the new design a quotient of the original design. Although the quotient is non binary and unequally replicated, it turns out to beE-optimal within the class of all proper and connected designs withb, k andv, provided the replication number of the optimal design we start with is not too large.     

A note on theE-optimality of block designs

Summary In this paper we consider the problem of determiningE-optimal block designs for experimental situations in whichv treatments are to be tested onn experimental units arranged inb blocks and where the block sizes and number of replications assigned to the treatments are allowed to vary. Some sufficient conditions are obtained for designs to beE-optimal in these situations and methods for constructing designs which satisfy the sufficient conditions given are also derived.     

A note on R-optimal designs for multiresponse models

This paper considers the optimal design problem for multiresponse regression models. The $R$ -optimality introduced by Dette (J R Stat Soc B 59:97–110, 1997) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the $R$ -optimality is provided for multiresponse models. Illustrative examples of the $R$ -optimal designs for two multiresponse models are presented based on the general equivalence theorem.     

On the construction of <Emphasis Type="Italic">E</Emphasis>(<Emphasis Type="Italic">s</Emphasis><Superscript>2</Superscript>)-optimal supersaturated designs

Supersaturated designs are an important class of factorial designs in which the number of factors is larger than the number of runs. These designs supply an economical method to perform and analyze industrial experiments. In this paper, we consider generalized Legendre pairs and their corresponding matrices to construct E(s ²)-optimal two-level supersaturated designs suitable for screening experiments. Also, we provide some general theorems which supply several infinite families of E(s ²)-optimal two-level supersaturated designs of various sizes.      

Design of optimal step�Cstress accelerated life tests under progressive type I censoring with random removals

This paper considers the analysis of exponential distributed lifetime data observed under k-stage step?Cstress accelerated life test under progressive type I censoring with random removal (PCRR), where the number of units removed at each stress follows a binomial distribution. We compute the expected Fisher information matrix of the maximum likelihood estimator of the log mean life at design (use) stress. The problem of choosing the optimal time ?? _i , i = 1, . . . , k ? 1 under k-stage step?Cstress is addressed using variance (V)-optimality as well as determinant (D)-optimality criteria. An illustrative example is provided with discussion.     

SomeE andMV-optimal row-column designs having equal numbers of rows and columns

In this paper we consider experimental situations in whichv treatments are to be tested using a row-column design consisting ofb columns andb rows and wherev does not divideb ². Some sufficient conditions are obtained for a design to beE orMV-optimal in such an experimental setting and methods for constructing row-column designs satisfying the sufficient conditions obtained are also given. This research was supported by NSF Grant No. DMS-8401943.     

The accuracy of IMF crises nowcasts

The International Monetary Fund (IMF) provides loans to countries in economic crises as a lender of last resort. IMF loan approvals are tied to policy reforms and quantitative targets that reflect the IMF’s crisis assessment. An extensive literature scrutinizes the efficacy of IMF loan programs, instead, we examine the accuracy of the IMF’s crisis assessments (nowcasts) that predicate program designs. Analyzing an unprecedented 602 IMF loan programs from 1992 to 2019, we contradict previous findings that IMF nowcasts are generally optimistic. Disentangling the structure of the IMF’s nowcast bias, we find the IMF systematically overestimates high-growth recoveries GDPs, while low-growth recoveries for low-income countries (LICs) are underestimated. In contrast, non-LICs’ nowcasts exhibit no statistically significant optimistic and pessimistic bias. Interestingly, shorter nowcast horizons do not improve accuracy, and GDP growth nowcasts improved substantially since 2013, while inflation nowcasts remain inefficient. We also isolate the sources of IMF nowcast inefficiencies according to ((i) program objectives, ((ii) program conditionality type, ((iii) geographic regions, ((iv) global crises, and ((v) geopolitics (elections, conflicts, and disasters).     

Multi-level and mixed-level <Emphasis Type="Italic">k</Emphasis>-circulant supersaturated designs

Supersaturated designs (SSDs) constitute an important class of fractional factorial designs that could be extremely useful in factor screening experiments. Most of the existing studies have focused on balanced designs. This paper provides a new lower bound for the \(E(f_{NOD})\)-optimality measure of SSDs with general run sizes. This bound is a generalization of existing bounds since it is applicable to both balanced and unbalanced designs. Optimal multi and mixed-level, balanced and nearly balanced SSDs are constructed by applying a k-circulant type methodology. Necessary and sufficient conditions are introduced for the generator vectors, in order to pre-ensure the optimality of the constructed k-circulant SSDs. The provided lower bounds were used to measure the efficiency of the generated designs. The presented methodology leads to a number of new families of improved SSDs, providing tools for directly constructing optimal or nearly-optimal k-circulant designs by just checking the corresponding generator vector.     

Optimal block designs for diallel crosses

Dey and Midha (Biometrika 83(2):484–489, 1996) constructed optimal block designs for complete diallel cross experiment using triangular partially balanced incomplete block designs with two associate classes. They listed optimal block designs for the lines in the range from 5 ≤ v ≤ 10. In this paper, we are also proposing additional optimal block designs for complete diallel cross experiment using two associate class partially balanced block designs for some additional values of v. Our method yields designs for proper and non-proper settings for complete diallel cross experiments. The proper and non proper designs are optimal in the sense of Kempthorne (Genetics 41:451–459, 1956) and non-proper designs are universally optimal in the sense of Kiefer (A survey of statistical design and linear models, North Holland, Amsterdam, 1975). The list of practically important designs is also given.     

Comparison of test vs. control treatments using distance optimality criterion

We consider the problem of comparison of one test treatment (τ₀) with a set of v control treatments (τ₁, τ₂, …, τ_v) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings. It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design. Received: December 1999     

A reference-dependent representation with subjective tastes

Experimental and empirical evidence documents instances where the presence of an inferior option in a menu increases the attractiveness of the better options from that menu and thus distorts the normative ranking across menus. We analyze the case when in addition to this so called context-effects bias there is also a concern for flexibility, in the spirit of the literature initiated by Kreps (1979) and Dekel et al. (2001). Since the context-effects bias and the desire for flexibility both increase the inclination of a decision maker to choose larger menus, our analysis allows the disentangling of the effect of the behavioral bias from the effect of the rational desire from flexibility. We find a weak condition on the set of ex post preferences under which the two effects are identifiable. We show that our representation is essentially unique. From a methodological viewpoint, our paper provides a novel technique of identifying probabilities on the state space of subjective uncertainty introduced by Dekel et al. (2001) when this state space is infinite. This method renders the infinite state space essentially finite with respect to a certain salient property.     

Efficient discriminating design for a class of nested polynomial regression models

This paper studies efficient designs for simultaneous model discrimination among polynomial regression models up to degree k. Based on the -optimality criterion proposed by Dette (Ann Stat 22:890–903, 1994), a maximin -optimal discriminating design is derived in terms of canonical moments for . Theoretical and numerical results show that the proposed design performs well for model discrimination in most of the considered models.     

A general construction of E(s 2)-optimal large supersaturated designs

A general method for construction of E(s ²)-optimal, two-level supersaturated designs (SSDs) with the equal occurrence property, from supplementary difference sets is introduced. It is proved that SSDs constructed in this way are E(s ²)-optimal. Comparisons are made with previous works and it is shown that the proposed method gives promising results for the construction of E(s ²)-optimal large SSDs.     

Minimal efficiency of designs under the class of orthogonally invariant information criteria

Consider the linear regression model with uncorrelated errors and an experimental design . In the article, we address the problem of calculating the minimal efficiency of with respect to the class of orthogonally invariant information criteria, containing all Kiefers criteria of _p-optimality, among others. We show that the -minimal efficiency of is equal to the minimal efficiency of with respect to a finite class of criteria which generalize the criterion of E-optimality. We also formulate conditions under which a design is maximin efficient, i.e. the most efficiency-stable for criteria from . To illustrate the results, we calculated the -minimal efficiency of _p (in particular D, A and E) optimal designs for polynomial regression on [–1,1] up to degree 4. Moreover, for the quadratic model we explicitly constructed the -maximin efficient design.Acknowledgement. The author would like to thank prof. Pázman as well as an anonymous referee for useful and inspiring comments on earlier versions of this article.Supported by: VEGA grant of the Slovak Agency No. 1/0264/03