Planning studies with an optimal control multisectoral dynamic economic model: The case of Sri Lanka

This article investigates the impact of different development scenarios on optimal investment strategy and economy of Sri Lanka and studies the potential of applying control theory techniques to economic planning. The multisectoral dynamic planning model is formulated as a linear quadratic tracking problem. Targets to be tracked define the development strategies: economic growth, trade deficit reduction, food self-sufficiency, and balanced growth. Besides providing insights into these strategies, empirical results show that the difficulty in setting inequality constraints and ensuring nonnegative solutions could undermine the linear tracking optimal control technique for development planning.     

Robust estimation in certain heteroscedastic linear models when there are many parameters

We study estimation of regression parameters in heteroscedastic linear models when the number of parameters is large. The results generalize work of Huber (1973), Yohai and Maronna (1979), and Carroll and Rupert (1982a).     

Robust designs and optimality of least squares for regression problems

Unbiased linear estimators are considered for the model

$\text{Y(}\text{x}{}_{\mathrm{i}}\text{)=θ}{}_0\text{+}\text{∑k}\text{j=1}\text{θ}{}_{\mathrm{j}}\text{x}{}_{\mathrm{ij}}\text{+ψ(}\text{x}{}_{\mathrm{i}}\text{)+ε}{}_{\mathrm{i}}\text{, i=1,2,…,n,}$

where ψ(x) is an unknown contamination. It is assumed that |ψ(x)|?φ(6x6) where φ is a convex function. Minimax analogues of Φ_p-optimality criteria are introduced. It is shown that, under certain (sufficient) conditions, the least squares estimators and corresponding designs are optimal in the class of all unbiased linear estimators and designs. It is also shown that, in the case when least squares estimators with symmetric design do not lead to an optimal solution, the relative efficiency of optimal least squares is not diminishing and has a uniform lower bound.     

Generalized Bhaskar Rao designs of block size three

We show that the necessary conditions

$\text{λ≡0 (}\text{mod}\text{|G|)}$

,

$\text{λ(υ?1)≡0 (}\text{mod}\text{2)}$

,

$\text{λυ(υ?1)≡}\text{0 (}\text{mod}\text{6)}\text{for}\text{|G|}\text{odd}\text{,}\text{0 (}\text{mod}\text{24)}\text{for}\text{|G|}\text{even}$

, are sufficient for the existence of a generalized Bhaskar Rao design GBRD(υ,b,r,3,λ;G) for the elementary abelian group G, of each order |G|.     

Gaussian approximation of signed rank statistics process

We consider the signed linear rank statistics of the form

$\text{S}{}_{\mathrm{\Delta N}}\text{=}\text{∑}\text{i=1}\text{N}\text{c}{}_{\mathrm{Ni}}\text{ø(}\text{R}{}^{\mathrm{\Delta }}{}_{\mathrm{Ni}}\text{(N+1)}\text{)}\text{sgn}\text{Y}{}^{\mathrm{\Delta }}{}_{\mathrm{Ni}}$

where the c_Ni's are known real numbers, Δ∈[0,1] is an unknown real parameter,R^Δ_Ni is the rank of |Y^Δ_Ni| among |Y^Δ_Nj|, 1≤j≤N, ø is a score generating function, sgn y=1 or -1 according as y≥0 or <0, and Y^Δ_Nj, 1≤j ≤N, are independent random variables with continuous cumulative distribution functions F(y?Δd_Nj), 1≤ j≤N, respectively where the d_fNi's are known real numbers. Under suitable assumptions on the c's, d's, φ and F, it is proved that the random process {S_ΔN?S_0N?ES_ΔN, 0≤Δ≤1}, properly normalized, converges weakly to a Gaussian process, and this result is also true if ES_ΔN is replaced by Δb_N, where

$\text{b}{}_{\mathrm{N}}\text{=4}\text{∑}\text{i=1}\text{N}\text{c}{}_{\mathrm{Ni}}\text{d}{}_{\mathrm{Ni}}\text{∫}\text{0}\text{∞}\text{ø′(2F(x)?1)?}{}^2\text{(x)}\text{d}\text{x}\text{and}\text{?=F′}$

. As an application, we derive the asymptotic distribution of the properly normalized length of a confidence interval for Δ.     

The uniform convergence of the nadaraya-watson regression function estimate

If (X₁,Y₁), …, (X_n,Y_n) is a sequence of independent identically distributed R_d × R-valued random vectors then Nadaraya (1964) and Watson (1964) proposed to estimate the regression function m(x) = ? {Y₁|X₁ = x{ by where K is a known density and {h_n} is a sequence of positive numbers satisfying certain properties. In this paper a variety of conditions are given for the strong convergence to 0 of ess_Xsup|m_n (X)-m(X)| (here X is independent of the data and distributed as X₁). The theorems are valid for all distributions of X₁ and for all sequences {h_n} satisfying h_n → 0 and nh/log n→0.     

On a random series in a hilbert space

Let (S_n) be partial sums of a non-degenerate sequence of Identically and independently distributed random variables taking values in a separable Hilbert space. Then for 0 ≤ β ≤ 3/2, the series converges almost nowhere. For β > 3/2 this may not be true.     

On the non-Markovian structure of discrete order statistics

In this note we show that the Markov Property holds for order statistics while sampling from a discrete parent population if and only if the population has at most two distinct units. This disproves the claim of Gupta and Gupta (1981) that for geometric parent, the order statistics form a Markov chain.     

Admissible estimators in finite population sampling employing various types of prior information

We consider some estimators of the total and variance of a finite population from Bayesian and pseudo-Bayesian perspectives. Recently, Meeden and Ghosh (1982a, 1982b) have provided quite simple but powerful tools for proving admissibility of estimators and estimator-design pairs is finite population sampling problems. We consider what these techniques yield in the way of admissibility results for the estimators discussed.