This paper addresses the informational asymmetry for con structing an ultrametric evolutionary tree from upper and lower bounds on pairwise distances between n given species We show that the tallest ultrametric tree exists and can be constructed in O n time while the existence of the shortest ultrametric tree depends on whether the lower bounds are ultrametric The tallest tree construction algo...

This paper constructs bounds on the minimax risk under loss functions when statistical estimation is performed in a distributed environment and with communication constraints. We treat this problem using techniques from information theory and communication complexity. In many cases our bounds rely crucially on metric entropy conditions and the classical reduction from estimation to testing. A n...

This paper examines various transmission mechanism channels on economic growth in Malaysia over the quarterly period 1980:1-2004:4 using bounds testing approach. The bounds test reveals evidence of cointegration between the real GDP and the real exchange rate and share prices that address the exchange rate and asset price channels as the key transmission mechanisms in the conduct of the monetar...

‎let $g$ be a finite group and $d_2(g)$ denotes the probability ‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$‎. ‎we ‎will obtain lower and upper bounds for $d_2(g)$ in the case where ‎the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for ‎all $xin g$‎. ‎also the given examples illustrate that all the ‎bounds are sharp.

We address the problem of goodness-of-fit testing for Hölder continuous densities under local differential privacy constraints. study minimax separation rates when only non-interactive mechanisms are allowed to be used and both sequentially interactive can privatisation. propose associated procedures whose analysis enables us obtain upper bounds on rates. These results complemented with lower b...

It is shown that the aliasing probability is bounded above by (1 + E ) / L M 1/L ( E small for large L) for test lengths L less than the period, L,, of the signature polynomial; for test lengths L that are multiples of L,, the aliasing probability is bounded above by 1; and, for test lengths L greater than L, and not a multiple of L,, the aliasing probability is bounded above by 2 / ( L c + 1)....

Two alternative exact characterizations of the minimum error probability of Bayesian M -ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy, Poor and Verdú; the second expression is function of an information-spectrum measure and implies the tightness...

In the distribution-free property testing model, the distance between functions is measured with respect to an arbitrary and unknown probability distribution D over the input domain. We consider distribution-free testing of several basic Boolean function classes over {0, 1}, namely monotone conjunctions, general conjunctions, decision lists, and linear threshold functions. We prove that for eac...

In the setting of non-commutative arithmetic computations, we define a class of circuits that generalize algebraic branching programs (ABP). This model is called unambiguous because it captures the polynomials in which all monomials are computed in a similar way (that is, all the parse trees are isomorphic). We show that unambiguous circuits of polynomial size can compute polynomials that requi...

We introduce strong, and in many cases optimal, lower bounds for the number of queries required to nonadaptively test three fundamental properties of functions f : [n] → R on the hypergrid: monotonicity, convexity, and the Lipschitz property. Our lower bounds also apply to the more restricted setting of functions f : [n]→ R on the line (i.e., to hypergrids with d = 1), where they give optimal l...