Extension and necessity of Cheng and Wu conditions

Repeated Measurement Designs, with two treatments, n (experimental) units and p periods are examined. The model examined is with uncorrelated observations following a continuous distribution with constant variance and the parameters of interest are (i) the difference of direct effects and (ii) the difference of residual effects. In this paper (a) the difference of Universal optimality and Φ-optimality is clarified and (b) the sufficient conditions of Cheng and Wu (1980) are extended to include the case n=2 mod 4, p even, (c) also it is shown that these conditions are also necessary for Φ-optimality for estimating direct as well as residual effects, and (d) a method is proposed to construct Φ-optimal designs and examples are given when n even and p=3, n=0 mod 4 and p=4, n=2 mod 4 and p=4. In the last case the estimated parameters in the optimal design are correlated.     

Bad Probability,Good Statistics,and Group Testing for Binomial Estimation

This article examines some improperly stated but often used textbook probability problems. Moving from a probabilistic to a statistical setting provides insight into group testing (i.e., observing only whether one or more of a group responds and not the response of each individual). Exact methods are used to construct tables showing (i) that group testing n times to estimate p can be more efficient than n individual tests even for small n and large p, (ii) optimal grouping strategies for various (n, p) combinations, and (iii) the efficiencies and biases achieved.     

Construction of Neighbor-Balanced Designs in Linear Blocks

Neighbor-balanced designs are useful to remove the neighbor effects in experiments where the performance of a treatment is affected by the treatments applied to its adjacent neighbors. In this article, neighbor-balanced designs are constructed in linear blocks of (i) equal sizes and (ii) two different sizes k ₁ and k ₂.     

Some determinant optimality aspects of main effect fold-over designs

Saha and Mohanty (1970) presented a main effect fold-over design consisting of 14 treatment combinations of the 24×33 factorial, which had the nice property of being even balanced. Calling this design DSM, this paper establishes the following specific results: (i) DSM is not d-optimal in the subclass Δe of all 14 point even balanced main effect fold-over designs of the 24×33 factorial; (ii) DSM is not d-optimal in the subclass $\text{Δ}{}^1\text{?Δ}{}^{\mathrm{e}}$ of all 14 point even and odd balanced main effect fold-over designs of the 24×33 factorial; (iii) DSM is even optimal in $\text{Δ}{}^1$ and Δe. In addition to these results two 14 point designs in $\text{Δ}{}^1$ are presented which are d-optimal and via a counter example it is shown that these designs are not odd optimal. Finally, several general matrix algebra results are given which should be useful in resolving d-optimality problems of fold-over designs of the kn11×kn22 factorial.     

A-optimal design measures for one-way layouts with additive regression

For linear models with one discrete factor and additive general regression term the problem of characterizing A-optimal design measures for inference on (i) treatment effects, (ii) the regression parameters and (iii) all parameters will be considered. In any of these problems product designs can be found which are optimal among all designs, and equal weigth 1/J may be given to each of the J levels of the discrete factor. For problem (i) and (ii) the allocation of the continuous factors for the regression term should follow a suitable optimal design for the corresponding pure regression model, whereas for problem (iii) this would not give an A-optimal product design. For this problem an equivalence theorem for A-optimal product designs will be given. An example will illustrate these results. Finally, by analyzing a model with two discrete factors it will be shown that for enlarged models the best product designs may not be A-optimal.     

The Concept of Majorization in Experimental Design

Row and column designs are examined and the concept of majorization is applied to find optimal designs, when the observations are either independent or dependent. The dependence follows a first-order autoregression with parameter α. The case of two treatments is examined and the universally optimal or Φ-optimal designs are given, for different values of a, when the number of experimental units is even or odd. A filtering procedure is followed to reduce the number of competing designs.     

An optimal k of kth MA-ARIMA models under MA(q) models

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated MA(q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that, 5th Exponential Weighted Moving Average (5-th EWMA) Autoregressive Integrated Moving Average (ARIMA) model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM), stock market real data reveals the similar results of the simulation study.     

Construction of circular partially balanced-Repeated measurement designs using cyclic shifts

Repeated measurement designs are widely used in medicine, pharmacology, animal sciences and psychology. These designs balance out the residual effects. The situations where balanced repeated measurements designs require a large number of the subjects, partially-balanced repeated measurements designs should be used. In this paper some infinite series are developed which provide circular partially-balanced repeated measurement designs for p (periods) even. Catalogues of circular partially-balanced repeated measurement designs are also presented for v (treatments) ≤ 100 with p = 5, 7 & 9.     

An optimal k of kth MA-ARIMA models under a class of ARIMA model

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated ARIMA(p, d, q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that 5th exponential weighted moving average (5th EWMA) ARIMA model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM) stock market, real data reveal the similar results of simulation study.     

Combination-Based Permutation Tests: Equipower Property and Power Behavior in Presence of Correlation

Multivariate combination-based permutation tests have been widely used in many complex problems. In this paper we focus on the equipower property, derived directly from the finite-sample consistency property, and we analyze the impact of the dependency structure on the combined tests. At first, we consider the finite-sample consistency property which assumes that sample sizes are fixed (and possibly small) and considers on each subject a large number of informative variables. Moreover, since permutation test statistics do not require to be standardized, we need not assume that data are homoscedastic in the alternative. The equipower property is then derived from these two notions: consider the unconditional permutation power of a test statistic T for fixed sample sizes, with V ? 2 independent and identically distributed variables and fixed effect δ, calculated in two ways: (i) by considering two V-dimensional samples sized m₁ and m₂, respectively; (ii) by considering two unidimensional samples sized n₁ = Vm₁ and n₂ = Vm₂, respectively. Since the unconditional power essentially depends on the non centrality induced by T, and two ways are provided with exactly the same likelihood and the same non centrality, we show that they are provided with the same power function, at least approximately. As regards both investigating the equipower property and the power behavior in presence of correlation we performed an extensive simulation study.     

Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T^{? 1}), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)^{? 1/2} or n^{? 1/2}. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.     

Correlation estimation in Downton's bivariate exponential distribution using incomplete samples

Suppose (X, Y) has a Downton's bivariate exponential distribution with correlation ρ. For a random sample of size n from (X, Y), let X _r:n be the rth X-order statistic and Y _[r:n] be its concomitant. We investigate estimators of ρ when all the parameters are unknown and the available data is an incomplete bivariate sample made up of (i) all the Y-values and the ranks of associated X-values, i.e. (i, Y _[i:n]), 1≤i≤n, and (ii) a Type II right-censored bivariate sample consisting of (X _i:n , Y _[i:n]), 1≤i≤r<n. In both setups, we use simulation to examine the bias and mean square errors of several estimators of ρ and obtain their estimated relative efficiencies. The preferred estimator under (i) is a function of the sample correlation of (Y _i:n , Y _[i:n]) values, and under (ii), a method of moments estimator involving the regression function is preferred.     

An optimal k of kth MA-ARIMA models under AR(p) models

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated autoregressive AR(p) model. We run a simulation using the three above examining method under specific conditions. The main finding is that the optimal k = 4 and then k = 3. Especially, the fourth WMA ARIMA model, fourth EWMA ARIMA model, and third EWMA ARIMA model are the best forecasting models among others, respectively. For all the six real data reveal the similar results of simulation study.     

On the E-optimality of blocked main effects plans in blocks of different sizes

In this article, we consider experimental situations in which m 2-level factors are to be studied using a main effects plan where n runs are to be partitioned into b blocks having both even and odd sizes. For these cases, we give some simple methods for constructing E-optimal designs.     

Nonparametric Estimation of the Average Availability

The average availability of a repairable system is the expected proportion of time that the system is operating in the interval [0, t]. The present article discusses the nonparametric estimation of the average availability when (i) the data on ‘n’ complete cycles of system operation are available, (ii) the data are subject to right censorship, and (iii) the process is observed upto a specified time ‘T’. In each case, a nonparametric confidence interval for the average availability is also constructed. Simulations are conducted to assess the performance of the estimators.     

TABLES OF SMALL OPTIMAL REPEATED MEASUREMENTS DESIGNS

This paper presents tables of the optimal repeated measurements designs for the estimation of direct effects and of residual effects for a model with independent errors, for up to n = 10 experimental units, for t= 2 treatments and p= 2, 3 or 4 periods, and for t= 3 treatments and p= 2 or 3 periods.     

Efficient crossover designs in the presence of interactions between direct and carry-over treatment effects

Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period.A particular class of strongly balanced repeated measurements designs with n=t² units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2t.     

A Bivariate Optimal Replacement Policy for a System With Age-dependent Minimal Repair and Cumulative Repair-cost Limit

In this article, a repairable system with age-dependent failure type and minimal repair based on a cumulative repair-cost limit policy is studied, where the information of entire repair-cost history is adopted to decide whether the system is repaired or replaced. As the failures occur, the system has two failure types: (i) a Type-I failure (minor) type that is rectified by a minimal repair, and (ii) a Type-II failure (catastrophic) type that calls for a replacement. We consider a bivariate replacement policy, denoted by (n,T), in which the system is replaced at life age T, or at the n-th Type-I failure, or at the kth Type-I failure (k < n and due to a minor failure at which the accumulated repair cost exceeds the pre-determined limit), or at the first Type-II failure, whichever occurs first. The optimal minimum-cost replacement policy (n,T)* is derived analytically in terms of its existence and uniqueness. Several classical models in maintenance literature could be regard as special cases of the presented model. Finally, a numerical example is given to illustrate the theoretical results.     

Minimal balanced repeated measurements designs

Experimental designs in which treatments are applied to the experimental units, one at a time, in sequences over a number of periods, have been used in several scientific investigations and are known as repeated measurements designs. Besides direct effects, these designs allow estimation of residual effects of treatments along with adjustment for them. Assuming the existence of first-order residual effects of treatments, Hedayat & Afsarinejad (1975) gave a method of constructing minimal balanced repeated measurements [RM(v,n,p)] design for v treatments using n=2v experimental units for p [=(v+1)/2] periods when v is a prime or prime power. Here, a general method of construction of these designs for all odd v has been given along with an outline for their analysis. In terms of variances of estimated elementary contrasts between treatment effects (direct and residual), these designs are seen to be partially variance balanced based on the circular association scheme.     

Evidence of spurious regression driven by heavy-tailed observations with structural changes

This article extends the theoretical analysis of spurious relationship and considers the situation where the deterministic components of the processes generating individual series are independent heavy-tailed with structural changes. It shows when those sequences are used in ordinary least-square regression, the convenient t-statistic procedures wrongly indicate that (i) the spurious significance is established when regressing mean-stationary and trend-stationary series with structural changes, (ii) the spurious relationship occurs under broken mean-stationary and difference-stationary sequences, and (iii) the extent of spurious regression becomes stronger between difference-stationary and trend-stationary series in the presence of breaks. The spurious phenomenon is present regardless of the sample size and structural breaks taking place at the same points or not. Simulation experiments confirm our asymptotic results and reveal that the spurious effects are not only sensitive to the relative location of structural changes with the sample, but seriously depend on the stable indexes.